Numerical: Mensuration 2D — Triangles & Quadrilaterals MCQ — 15 Practice Questions with Answers

Explanation

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.

Explanation

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.

Explanation

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.

Explanation

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.

Explanation

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.