MCQ
Numerical: Mensuration 2D — Triangles & Quadrilaterals MCQ - Practice Questions with Answers
Solve 15 Numerical: Mensuration 2D — Triangles & Quadrilaterals questions for RAS/RPSC preparation.
Practice questions
Q1A parallelogram has adjacent sides of 13 cm and 8 cm. The height on the 13 cm side is 6 cm. Which pair of statements is correct? 1. Its area is 78 cm². 2. Its perimeter is 42 cm. 3. Its area is 48 cm².
The area of a parallelogram is base × corresponding height. The base given with its height is 13 cm, and the height on it is 6 cm. So, area = 13 × 6 = 78 cm²; statement 1 is correct. The perimeter of a parallelogram is 2 × (sum of adjacent sides) = 2 × (13 + 8) = 2 × 21 = 42 cm; statement 2 is correct. Statement 3 uses 8 × 6, which is not the corresponding base-height pair.
Q2Match each figure in List 1 with its area in List 2. List 1: 1. triangle with base 16 cm and height 9 cm; 2. rectangle 11 cm × 8 cm; 3. square of side 9 cm; 4. parallelogram with base 14 cm and height 6 cm. List 2: A. 88 cm²; B. 81 cm²; C. 84 cm²; D. 72 cm².
Find each area separately. For the triangle, area = 1/2 × 16 × 9 = 8 × 9 = 72 cm², so 1-D. The rectangle area is 11 × 8 = 88 cm², so 2-A. The square area is side² = 9 × 9 = 81 cm², so 3-B. The parallelogram area is base × height = 14 × 6 = 84 cm², so 4-C. Therefore, the correct matching is 1-D, 2-A, 3-B, 4-C.
Q3The base of a triangle is 24 cm and its corresponding height is 15 cm. What is its area?
The area of a triangle is 1/2 × base × height. Here, the base is 24 cm and the corresponding height is 15 cm. So, area = 1/2 × 24 × 15. First, 24 ÷ 2 = 12, and then 12 × 15 = 180. Therefore, the area of the triangle is 180 cm². The height must correspond to the given base, which is already stated in the question.
Q4Assertion: The area of a square whose diagonal is 10√2 cm is 100 cm². Reason: In a square, side = diagonal ÷ √2. Choose the correct option.
In a square, diagonal = side × √2, so side = diagonal ÷ √2. The given diagonal is 10√2 cm. Therefore, side = 10√2 ÷ √2 = 10 cm. The area of a square is side², so area = 10² = 100 cm². Thus, the assertion is true. The reason is also true because it gives the exact relation used to find the side from the diagonal, so it correctly explains the assertion.
Q5A trapezium has parallel sides of 14 cm and 26 cm, and its height is 9 cm. Which statement is incorrect?
For a trapezium, area = 1/2 × (sum of parallel sides) × height. The parallel sides are 14 cm and 26 cm, so their sum is 14 + 26 = 40 cm. Half of this sum is 20 cm. Area = 20 × 9 = 180 cm². Therefore, the statements giving 40 cm, 20 cm and 180 cm² are correct. The statement that the area is 360 cm² is incorrect.
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More questions
6A trapezium has parallel sides of 17 cm and 11 cm, and the distance between them is 8 cm. Which of the following statements is incorrect?
7In a trapezium, the parallel sides are 18 cm and 26 cm, and the distance between them is 10 cm. Which statement is correct?
8A rhombus has diagonals of 18 cm and 14 cm. Identify the correct area of the rhombus.
9In a rhombus, the diagonals are 18 cm and 24 cm. Which option gives its correct area?
10The area of a parallelogram is 168 cm². The height corresponding to its base is 12 cm, and the adjacent side is 9 cm. What is its perimeter?
11Assertion: The area of a rhombus whose diagonals are 24 cm and 10 cm is 120 cm². Reason: The area of a rhombus is 1/2 × product of its diagonals. Choose the correct option.
12Match each quantity with its correct value. 1. Area of a triangle with base 20 cm and height 7 cm. 2. Perimeter of a rectangle with length 12 cm and breadth 8 cm. 3. Area of a kite with diagonals 10 cm and 16 cm.
13Match each figure with its area: 1. Rectangle 13 cm × 7 cm, 2. Parallelogram with base 16 cm and height 9 cm, 3. Triangle with base 30 cm and height 8 cm.
14The base of a triangle is 16 cm and its corresponding height is 12 cm. What is its area?
15The base of a triangle is 24 cm and its area is 180 cm². What is its corresponding height?