Find the area of a triangle two sides of which are 16 cm and 22 cm and the perimeter is 64 cm. The vertex angle is the angle between the legs.

Find the area of a triangle two sides of which are 16 cm and 22 cm and the perimeter is 64 cm cm. Furthermore, the solved If two sides of a triangle are 8 cm and 6 cm and its perimeter is 26 cm. Just enter the known values and get instant results for any triangle. Heron's formula, also known as Hero's formula, is the formula to calculate triangle area given three triangle sides. Find the perimeter of an equilateral triangle with side length 12 meters. Input base and height or sides for instant results. Use the 45-45-90 triangle to find the height. If a, b, c are the sides of the triangle, then the perimeter of triangle = (a + b +c) units. How are they calculated and related formulae for isosceles and equilateral triangle? Find the perimeter of an isosceles triangle if the length of the two equal sides is 1. Perimeter of a triangle calculator online - easily calculate the perimeter of any triangle using different rules: side-side-side, side-angle-side, angle-side-angle, side-side-angle Supports many imperial and metric units: mm, cm, meters, km, inches, feet, yards, miles, and more. Find the perimeter of a rectangle with length 8 cm and width 5 cm. How to find the perimeter and area of a triangle? A triangle is a shape with three straight sides and three angles. If the base of the triangle is 24 cm, calculate the perimeter and the area of the triangle. Mar 23, 2019 · Find the area of an isosceles triangle whose one side is 10 cm greater than each of its equal sides and perimeter is 100 cm. The formula for the perimeter of a rectangle is often written as P = 2 l + 2 w, where l is the length of the rectangle and w is the width of the rectangle. Each of equal sides of an isosceles triangle is 4 cm greater than its height. 3). Also, calculate the altitude of the triangle corresponding to the shortest side. The length of the sides of a triangle are 5 cm,12 cm and 13 cm respectively. 23) Heron's formula is one of the most elegant solutions to finding the area of a triangle that doesn't contain a right angle. ) Heron's formula operates on any triangle where the length of each side is know. [Answer: 90 sq. Free triangle area calculator with step-by-step solutions. Calculate the area of any triangle. Find the third side of the triangle. also calculate the altitude of the triangle corrosponding to the shortest side. Hence the given triangle is a right-angled triangle whose hypotenuse is 17 cm, and one of the perpendicular sides is 15 cm. Two sides of a triangle are 15 cm and 20 cm. Calculate triangle area using base/height, three sides, or angles. Jun 9, 2018 · Find the area of triangle two sides of which are 16 cm and 22 cm and perimeter is 64 cm. Triangles are defined by six primary characteristics: three sides (a, b, c) and three angles (α, β, γ). The third side of the triangle is called the base. Instantly, you can learn that side b = 5 cm. A trapezoid is a 4-sided geometrical shape with two sides parallel to each other. The perimeter of a right is 40 cm and its hypotenuse measures 17. Nov 17, 2025 · Area and perimeter of a triangle, their units of measurement. It was first mentioned in Heron's book Metrica, written in ca. Question 4 Find the area of a triangle two sides of which are 18cm and 10cm and the perimeter is 42 cm. The perimeter of the triangle is 50 cm. A parallelogram is a quadrilateral with opposite sides parallel. This free triangle calculator computes the edges, angles, area, height, perimeter, median, as well as other values and a diagram of the resulting triangle. Determine the perimeter of a right triangle with legs 3 m and 4 m. The semi perimeter of a triangle is expressed in linear units like inches, yards, centimeters, and so on. 'Semi' means half, that is why the semi perimeter of a triangle is half the value of the perimeter. Isosceles Triangle Calculator The Isosceles Triangle Calculator helps you calculate any unknown value in an isosceles triangle—be it the equal sides (a), base (b), angles α and β, altitudes (ha, hb), area (A), or perimeter (P). Here we will discuss about the area and perimeter of the triangle. The angles with the base as one of their sides are called the base angles. 73) The hypotenuse and the semi-perimeter of a right triangle are 20 cm and 25 cm respectively. May 26, 2022 · Example 2 Find the perimeter of a triangle with sides measuring 6 cm, 8 cm, and 12 cm. Problems with detailed solutions are presented. Two forces 3 Two forces with magnitudes 8 Newtons and 15 Newtons act at a point. Calculate online the perimeter of a triangle, knowing all sides, two sides and the angle between them or one side and two adjacent to it angles. We can calculate the perimeter of any closed shape just adding up the length of each of the sides. The base of an isosceles triangle is 18 cm and its area is 108 cm². Sep 21, 2020 · The area of the **triangle **two sides are 18cm and 10cm and the perimeter is 42cm is **69. The total length of the boundary of a triangle can be calculated by adding the length of all its sides. To use the right angle calculator simply enter the lengths of any two sides of a right triangle into the top boxes. Feb 15, 2023 · Find the area of the triangle whose perimeter is 180 cm and two of its sides are of lengths 80 cm and 18 cm. Find the area Aug 1, 2025 · Calculator online for a rectangle. (Note: if more than 3 fields are filled, only a third used to determine the triangle, the others are (eventualy) overwritten 3 sides Find the area of a triangle, two sides of which are 8 cm and 11 cm and the perimeter is 32 cm. Also, trigonometric functions are used to find the area when we know two sides and the angle formed between them in a Find the area of a triangle having perimeter 32 cm, if one of its sides is equal to 11 cm, and the difference of the other two sides is 5 cm. (Use √2 = 1. Triangle calculator finds the values of remaining sides and angles by using Sine Law. लंबी है, तो शेष दो भुजाएँ ज्ञात कीजिए कि प्रिभुज का क्षेत्रफल अधिकतम हो। This triangle area calculator can help in determining the triangle area. Also, find the length of its altitude corresponding to the longest side. Why not give it a go? Check out also the twin brother of this calculator – parallelogram area calculator – to get to know this shape better. Learn more about the perimeter of the equilateral triangle with its definition, formulas, and solved examples. One of its diagonal measures Each pair of opposite sides of a parallelogram is congruent to each other. Use the Law of Cosines to calculate the length of the third side. A triangle has three sides and three angles. Area of a Triangle, A = 1/2 × b × h = 1/2 × 4 (cm) × 3 (cm) = 2 (cm) × 3 (cm) = 6 cm 2 Apart from the above formula, we have Heron’s formula to calculate the triangle’s area when we know the length of its three sides. 34cm2 55cm2 44cm2 54cm2 The perimeter of a right triangle is no different than the perimeter of any other shape. Oct 26, 2016 · The area of triangle is b) Given: Assume the triangle sides are a, b, and c. The result gives us the area of the triangle, which is approximately 176 cm^2. 45) Two adjacent sides of a parallelogram measures 5 cm and 3. Jul 7, 2018 · Step-by-step explanation: As per the data given in the question, we have to find the area of the triangle for the two sides. 10. Supports all triangle types and formulas. Area of triangle = (s (s a) (s b) (s c)) Here, s is the semi-perimeter, and a, b, c are the sides of the triangle Given a = 18 cm, b = 10 cm and Perimeter = 42 cm Semi-Perimeter = s Sep 12, 2024 · Example 1: Find the area of a triangle, two sides of which are 8 cm and 11 cm and the perimeter is 32 cm (see Fig. The other two sides (c and d) are called legs. Also calculate the altitude of the triangle corresponding to the shortest side . एक त्रिभुज का परिमाप 16 से. All internal angles of a trapezoid sum to give 360°. The perimeter of a right triangle is specifically for right-angled triangles only. (Triangles with a right angle or known altitude can make use of the simpler pythagorean theorem calculator. Also calculate altitude of triangle corresponding to the shortest side. When we decrease the length of the legs by 3 cm, then decrease its hypotenuse by 4 cm. P = 6 + 8 + 12 Answer: P = 26 centimeters An isosceles right triangle has area 32 cm², then hypotenuse is 8√2 cm. Perimeter of Triangle: The perimeter of any two-dimensional figure is defined as the distance around the figure. Given, Perpendicular (P) = 3 cm Base (B) = 4 cm Using Pythagoras theorem P2 + B2 = H2 (3)2 + (4)2 = H2 9 + 16 = H2 25 = H2 H = 5 Thus, the third side hypotenuse of the triangle ABC CA is 5 cm. Online calculators and formulas for an rectangles and other geometry problems. Measure the included angle (the angle between the two given sides). Not only have we implemented the easiest well-known equation but also two other parallelogram perimeter formulas. (Use √6 = 2. Referencing the triangle above: If a and b are given, If a and c are given, If b and c are given, An isosceles triangle is a triangle with two sides of equal length, called legs. 5) + 2 Right triangle calculator to calculate side lengths, hypotenuse, angles, height, area, and perimeter of a right triangle given any two values. Find the perimeter of the following swimming pool. Jan 7, 2025 · Suppose you must find an unknown side using the hypotenuse (13 cm) and a known side (12 cm). Find the perimeter and area of each parallelogram or triangle. Calculate the length of the third side Find the area of a triangle, two sides of which are 8 cm and 11 cm and the perimeter is 32 cm. Perimeter of a triangle formula, rules (laws), and calculation steps. Example: In your triangle, two sides are a = 8 cm and b = 10 cm long, and the included angle measures C = 45 degrees. A rectangle is a shape with opposite sides equal and all angles equal to 90 degrees. The length of two sides of a triangle are 12 cm and 15 cm. Right Triangle through sides: In the right triangle, knowing the two legs, and using the Pythagorean theorem, one can easily find the hypotenuse, hence substituting the perimeter formula, we get the above mentioned formula. Works with angles and radians! If you're searching for other formulas for the area of a quadrilateral, check out our dedicated quadrilateral calculator, where you'll find Bretschneider's formula (given four sides and two opposite angles) and a formula that uses bimedians and the angle between them. SAS triangle The triangle has two sides, long 7 and 19, and includes angle 47°24'. 1, 6 An isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cm. Enter the values of any two angles and any one side of a triangle below which you want to solve for remaining angle and sides. Free Isosceles Triangle Area & Perimeter Calculator - Calculate area, perimeter of an isosceles triangle step-by-step What is the perimeter of a square with 16 cm sides? How far around is a square that is 16 centimeters across? Use this easy and mobile-friendly calculator to compute the perimeter of a squire given the length of one side. Solution: Here, a = 5 cm, b = 12 cm and c = 13 cm ∴ s = 21 (a+b +c) = 21 (5+ 12+ 13) = 230 = 15 cm Let A be the area of the given triangle. Free Triangles calculator - Calculate area, perimeter, sides and angles for triangles step-by-step Equilateral triangle Perimeter = 3 × s Where s is the side length Right triangle You can use the Pythagorean Theorem to find the perimeter of a right triangle if you know, or can determine, the lengths of at least two sides from the given information. 41) The sides of triangle are 100 m, 120 m and 140 m. Continue reading to find out how to calculate the sides of a triangle for three different cases: If two sides and one angle are known; If two angles and one side are known; and If two sides and the perimeter are known. How to find the perimeter and area of a parallelogram? A parallelogram is a simple quadrilateral with two pairs of parallel sides. Find the area of a triangle whose sides are 9 cm, 12 cm, and 15 cm. Find the area of a triangle two whose sides are are 18 cm and 10 cm perimeter is 42 cm. It is the sum of all its sides, like a circumference. In Heron's formula, and most others, the sides of a triangle are typically denoted a Triangle Solver This triangle calculator is a tool designed to find the unknown characteristics of a triangle when provided with a sufficient set of known properties. Find its area. The Triangle Perimeter Calculator computes the perimeter using the lengths of the three sides of a triangle. Find the perimeter of a regular hexagon with side length 10 m. The calculator will then determine the length of the remaining side, the area and perimeter of the triangle, and all the angles of the triangle. Jan 3, 2019 · Find an answer to your question Find the area of the triangle two sides of which are 8 cm and 11cm and the perimeter is 32 CM Feb 24, 2021 · Find the area of triangle, two sides of which are 8cm, 11cm and the perimeter is 32cm ----------------------------------------------------- You may like to buy these books Step 1: Enter the values of any two angles and any one side of a triangle below for which you want to find the length of the remaining two sides. Dec 10, 2021 · Click here 👆 to get an answer to your question ️ Find the area of a triangle two sides of which are 18 cm and 10 cm and the perimeter is 42 cm. The area of a triangle is equal to 21√11cm^2 and one of its sides is 14cm. Nov 8, 2023 · Heron's formula is √s (s - a) (s - b) (s - c), where a, b, and c are the sides of the triangle, and s is the semi-perimeter of the triangle. 68 square **centimeters. Aug 15, 2020 · Solution : Two sides of a triangle are 16 cm & 22 cm . Find the perimeter of an isosceles right-angled triangle having an area of 5000 m². Find the area of a triangle two sides of which are 18cm and 10cm and the perimeter is 42cm. 5 cm. Jun 10, 2023 · To find the area of a triangle when two sides are given, we can use Heron's formula. These two sides (a and b in the diagram) are called the bases of the trapezoid. Just enter any two known values, and the calculator intelligently applies trigonometric and geometric formulas to solve the rest with step-by-step precision. The area of a triangle varies from one triangle to another depending on the length of the sides and the internal angles. Measure two side lengths of the triangle. Right angled triangle The hypotenuse of a right triangle is 17 cm long. How to calculate the angles and sides of a triangle? A triangle is determined by 3 of the 6 free values, with at least one side. Ex 10. Heron's formula states that the area (A) of a triangle with sides a, b, and c can be calculated using the semi-perimeter (s) as: Find the area of a triangle, two sides of which are 8 cm and 11 cm and the perimeter is 32 cm. Area of the triangle = √(s(s - a) ( Rectangle calculator, formula, work with steps, step by step calculation, real world and practice problems to learn how to find the area, perimeter & diagonal length of a rectangle in inches, feet, meters, centimeters and millimeters. Ans: Hint: In this question, we first need to write the relation between the sides of the triangle and the perimeter given by the formula \\ [P=a+b+c\\]. 61 cm 70cm2 and 4. a = 8 cm; b = 11 cm; and c = ? Perimeter = 32 cm To find: Triangle area = ? Step-by-step explanation: The formula for area of triangle is Where s = semi perimeter a, b, c are sides of triangle Semi-perimeter, Since, the perimeter = 32 cm So, The area of a triangle is the region enclosed within the sides of the triangle. Additionally, the angles on the same side of a leg are called adjacent and always sum up to 180 Find the area of triangle whose sides are 5 cm, 12 cm and 13 cm. Then third side of the triangle is The kite area calculator finds the area of a kite if you enter diagonals or two sides and the angle between them. Calculate the unknown defining areas, diagonals and angles with any three known variables. Triangle Definition A triangle is a closed figure with 3 angles, 3 sides, and 3 vertices. Use our free triangle calculator to find missing sides, angles, area, perimeter and more. Two sides of a triangle are 13 cm and 14 cm and its semi-perimeter is 18 cm. 1, 4 Find the area of a triangle two sides of which are 18 cm and 10 cm and the perimeter is 42 cm. Free Triangle Area & Perimeter Calculator - Calculate area, perimeter of a triangle step-by-step Perimeter of a triangle Here you will learn how to find the perimeter of a triangle, including what the perimeter is, how to calculate it and how to solve perimeter word problems. Omni's triangle side calculator allows you to calculate the length of the sides of a triangle. Between what two measures should the length of the third side fall? The base of an isosceles triangle is 24 cm and its area is 192 sq. Select two sides as the given parameters, and enter the hypotenuse c = 13 cm and side a = 12 cm. If you decrease both two legs by 3 cm, you will reduce the hypotenuse by 4 cm. Click here:point_up_2:to get an answer to your question :writing_hand:find the area of a triangle whose perimeter is 22 cm one side is 9 If you have ever wondered how to find the perimeter of a parallelogram, this parallelogram perimeter calculator can help you in no time. Area of triangle = √ (s (s−a) (s−b) (s −c)) Here, s is the semi-perimeter, and a, b, c are the sides of the triangle Given a = 8 cm, b = 11 cm and Perimeter = 32 cm Semi-Perimeter = s =Pe Find the area of the triangle whose perimeter is 180m and two of its sides are 80 cm and 18 cm. 64 cm 60 cm 63 cm 62 cm Use this similar triangles calculator to check whether two triangles are similar or to find the missing length of a similar triangle. Find the area of the shaded region. Students will first learn how to find perimeter as part of measurement and data in 3rd grade. 61 cm 30cm2 and 4. This guide explains how to calculate a triangle's perimeter, the formula used, and walks you through using our free online triangle perimeter calculator to solve geometry problems quickly and accurately. In the given figure, triangle ABC is an equilateral triangle having each side equal to 10 cm and triangle PBC is right angled at P in which PB = 8 cm. Example 1 Find the area of a triangle, two sides of which are 8 cm and 11 cm and the perimeter is 32 cm. The hypotenuse of a right triangle is 17 cm. The basic triangle area formula needs to have a base and height given, but what if we don't have it? See full list on calculator. What is the third side? The semi perimeter of a triangle is half the perimeter of a triangle. It gives the calculation steps. Ans: Hint:Here, we need to find the area of the triangle. Find the area of a triangle whose perimeter is 54 cm and two of its sides measure 12 cm and 25 cm. Fill in 3 of the 6 fields, with at least one side, and press the 'Calculate' button. Find the area of a triangle whose base is 6 cm and corresponding height is 4 cm. The following article explains what the hypotenuse is and how it is calculated using different parameters. Therefore, the correct choice is b). The perimeter of an equilateral triangle is the total length of its boundary. मी. It is one of the Question From - NCERT Maths Class 9 Chapter 12 SOLVED EXAMPLES Question – 1 HERONS FORMULA CBSE, RBSE, UP, MP, BIHAR BOARD QUESTION TEXT:- Find the area of a triangle, two sides of which are 8 Aug 23, 2021 · Find out area of triangle with our free online calculator! Calculate with base and height, but also with three different sides. 61 cm 62cm2 and 4. Find its perimeter. Easily calculate the area of any triangle using our Area of Triangles Calculator. Hence the length of the third side of triangle c = 14 c m Now to find the area of the triangle we will use the Heron’s formula which is given as A = s (s a) (s b) (s c) Here semi-perimeter s = a + b + c 2 , so by substituting the value of the length of the side of triangle we get s = 18 + 10 + 14 2 = 42 2 = 21 c m Triangle and its heights Calculate the length of the sides of the triangle ABC if v a =13 cm, v b =15 cm and side b are 5 cm shorter than side a. Click here:point_up_2:to get an answer to your question :writing_hand:find the area of a triangle whose perimeter is 22 cm one side is 9 Find the area of a triangle, two sides of which are 8 cm and 11 cm and the perimeter is 32 cm. The right triangle calculator will help you find the lengths of the sides of a right-angled triangle. Math Warehouse's popular online triangle calculator: Enter any valid combination of sides/angles (3 sides, 2 sides and an angle or 2 angle and a 1 side) , and our calculator will do the rest! It will even tell you if more than 1 triangle can be created. An easy to use area of a triangle calculator, which supports the basic height times side formula, as well as rules for solving triangles such as SSS, SAS, ASA, SSA, and the right-angled triangle hypotenuse by length of one of the other sides. Q. Solution: Here we have perimeter of the triangle = 32 cm a = 8 cm and b = 11 cm. Jul 23, 2025 · Example: If two sides of a right angled triangle are, AB (Perpendicular) = 3 cm and BC (Base) = 5 cm then find the third side Hypotenuse of the triangle. 60 AD, which was the collection of formulas for various objects' surfaces and volumes calculation. (Take √3= 1. Determine the length of these legs. The goal of solving a triangle is to determine the unknown sides and angles based on the given information. Find the area of the triangle. It is the sum of the three sides, the base, perpendicular, and the hypotenuse. Use the Pythagorean Theorem to find the length of the third side of Jun 11, 2025 · Calculate the perimeter of a triangle with sides 5 cm, 7 cm, and 10 cm. If the perimeter of a regular pentagon is 75 in, find the length of one side. Find the area of a triangle, two of its sides are 8cm and 11cm and the perimeter is 32cm. 8√30cm2 4√30cm2 15√2cm2 5√31cm2 The Pythagorean theorem calculator helps you find out the length of a missing leg or hypotenuse of a right triangle. The sides of triangle given: a = cm, b = cm Perimeter is cm As we know that, The perimeter of the triangle = () => => => => So, Semi Perimeter s = () Now, by using Heron's Formula, Area of triangle = Hence, the area of a Sep 23, 2016 · Find the area of a triangle whose perimeter is 180cm and 2 of its sides are 80cm and 18cm. Solution: It is given that Base of triangle = 6 cm Height of triangle = 4 cm We know that Area of triangle = ½ × base × height Substituting the values = ½ × 6 × 4 By further calculation = 6 × 2 = 12 cm 2 2. Perimeter of triangle, (P) = 64 cm Diagram : Let the third side of triangle be r cm; As we know that perimeter of triangle : Now; A = 16 cm B = 22 cm C = 26 cm & Thus; The area of triangle will be 32√30 cm² . The other two sides of the triangle are ____ and ____. If a tennis court has a perimeter of 210 ft and a length of 78 ft, find its width. Find area and perimeter of right triangles given hypotenuse, sides or any relations between these quantities. Find the length of perpendicular from the opposite vertex to the side whose length is 13 cm. Includes formulas, examples, and practical applications for geometry. Access ML Aggarwal Solutions for Class 9 Maths Chapter 16: Mensuration Exercise 16. है। यदि एक भुजा 6 से. P = 2 × a + b = 2 × (1. Apr 17, 2018 · find the area of a triangle whose perimeter is 180 cm and two of its sides are 80 cm and 18 cm. State true or false. = 9 cm Perimeter of the triangle = Sum of the sides. This triangle solver will also teach you how to find the area of a right triangle as well as give plenty of information about the practical uses of a right triangle. . Area of a Triangle Calculator finds from either 3 sides or from the base and the height. Find the size of its legs. Round to the nearest tenth if necessary. While we know by courtesy of the angle sum property that the sum of interior angles is 180°, the length of sides can be anything. Calculate the perimeter of a triangle and learn formulas for solving triangle perimeter using three sides or a mix of sides and angles. In the above example you could have also written P = 2 (3) + 2 (8) = 6 + 16 = 22 cm. Add the three side lengths together to find the perimeter. Calculate the perimeter of an isosceles triangle with two sides of 8 inches and a base of 5 inches. Solution Since all the sides are measured in centimeters, just add the lengths of all three sides to get the perimeter. Find the area of a triangle two sides of which are 8 cm and 11 cm and perimeter is 32 cm. 1 1. (Note: if more than 3 fields are filled, only a third used to determine the triangle, the others are (eventualy) overwritten 3 sides Find the area of an isosceles triangle, whose length of two equal sides is 5 cm and the length of the third side is 6 cm? Find the length of each side of a right isosceles triangle whose area is 112. Calculate the area of this triangle. Free Triangle Sides & Angles Calculator - Calculate sides, angles of a triangle step-by-step The hypotenuse and the semi-perimeter of a right triangle are 20 cm and 25 cm respectively. net Use our free Triangle Calculator to find missing sides, angles, perimeter, and area of any triangle. Find the area of a quadrilateral ABCD in which AD = 24 cm, ∠BAD = 900 and BCD forms an equilateral triangle whose each side is equal to 26 cm. The Pythagorean theorem calculator finds the length of the remaining two sides of a given triangle using sine law or definitions of trigonometric functions. Justify your answer. cm] If the length of equal sides of an isosceles triangle is 5 cm and base is 6 cm, then find its area using heron’s formula. Right triangle calculator to compute side length, angle, height, area, and perimeter of a right triangle given any 2 values. In this article, you will first learn about what is the perimeter, how to find the perimeter of different types of triangles when all side lengths are known. To find the area of the triangle, we can use Heron's formula. Let the length of the other perpendicular side be x, then by Pythagoras theorem, Transcript Ex 10. Additionally, it can calculate the kite's perimeter. 61 cm Find the area of an isosceles triangle, each of whose equal sides is 13 cm and base 24 cm. h is the height of the trapezoid. The area of a triangle is expressed in square units, like, m 2, cm 2, in 2, and so on. 52cm2 and 4. The triangle length calculator tells you the length of the third side if you enter two sides and an angle. Find the area of a triangle whose two sides are 18 cm and 10 cm and the perimeter is 42 cm. Jan 14, 2023 · Notice that the perimeter of a rectangle always has two pairs of equal length sides. 5 cm and the length of the third side is 2 cm. The perimeter of a triangle ABC = AB + BC + CA = 2 cm + 4 cm + 3 cm, (add the length of each side of the triangle). 5 cm 2. cm find the area of the area of the triangle . The vertex angle is the angle between the legs. Find the area of an isosceles triangle whose one side is 10 cm greater then its equal side and its perimeter is 100 cm ( Take √5= 2. Aug 1, 2025 · Calculations include side lengths, corner angles, diagonals, height, perimeter and area of parallelograms. rmetvd ywaksk hppvr btagny iuvlsasw rgwrp mdwkj apg moekvm odpgkw vjeb qovlqk abrb knllq pvhf