Arithmetic Aptitude - Area and Peimeter of Triangles - questions with answers

1. You are required to calculate the area of a scalene triangle. Which of the following set is sufficient to calculate the same?
   

   I: Perimeter of the triangle

   II: Measure of one side of the triangle

   III: Two sides of the triangle and the perimeter

   IV: One side of the triangle and the perimeter

   1. Only II
   2. Only I
   3. Only IV
   4. Only III

   View Answer

   Answer: D. Only III



2. For the given image, calculate the area of the shaded portion:
   

   b1 = 6; b2 = 7; b3 = 2; b4 = 5;

   

   1. 7.5 m²
   2. 5 m²
   3. 6 m²
   4. 5.5 m²

   View Answer

   Answer: A. 7.5 m²

   Explanation: Area of triangle 1 + Area of triangle 2
   = (5 * 2)/ 2 + (5 *1 )/2 = 7.5 m²

   
   
3. The sides of the triangle are as shown in the figure. If the perimeter is 71 m, find the length of the longest side of the triangle?
   

   

   1. 36
   2. 38
   3. 30
   4. 32

   View Answer

   Answer: B. 38

   Explanation: Perimeter of a triangle is the sum of all the sides of the triangle:
   3x + 1 + 5x + 8 + 2x + 2 = 71
   10 x + 11 = 71
   10 x = 60
   x = 6
   

   
   
4. The sides of a triangle are as shown in the figure. The perimeter is 60m. Which of the following is the right equation to solve this problem?
   

   

   1. 6x + 3 = 60
   2. 3(2x+1) = 60
   3. 3 (2x +3) = 60
   4. 6x + 6 = 60

   View Answer

   Answer: D. 6x + 6 = 60

   Explanation: Perimeter of a triangle is the sum of all its sides. In this case, each side is 2x + 2.
   Hence, 3 (2x +2) = 6x + 6 = 60 is the correct equation.

   
   
   
5. If x = 3y and the perimeter of the triangle is 80, find the measure of the shortest and the longest side?
   
   

   

   1. 20, 28
   2. 22, 34
   3. 28, 32
   4. 20, 32

   View Answer

   Answer: D. 20, 32

   Explanation: Given x = 3y
   Perimeter of a triangle is the sum of all its sides. Hence,
   2x + y + 2x + 2y + x + 2y = 80
   5x + 5y = 80
   5 (3y) + 5y = 80
   20 y = 80
   y = 4
   x = 3 * 4 = 12
   side 1: 2x + y = 2(12) + 4 = 28
   side 2: x + 2y = 12 + 2(4) = 12 + 8 = 20 (shortest)
   side 3: 2x+2y = 2(12) + 2(4) = 24 + 8 = 32 (longest)
   



6. Find the sides of the given equilateral triangle if the area is 43.3 cm²?
   

   

   1. 8
   2. 10
   3. 12
   4. 20

   View Answer

   Answer: B. 10

   Explanation: Area of an equilateral triangle is √3/4 a²
   Given area is 43.3 cm².
   Therefore, √3/4 a² = 43.3
   Hence, a = 10 cm