Question

In the following questions, two statements (i) and (ii) are given. Choose the valid statement.

1. Area of a trapezium = `1/2` × sum of parallel sides × distance between parallel sides.
2. A square is inscribed in a circle of radius 14 cm. The area of square is 196 cm².

Options

• Only (i)

• Only (ii)

• Both (i) and (ii)

• Neither (i) nor (ii)

Answer 1

Only (i)

Explanation:

(i) True: Area of a trapezium = `1/2` × (Sum of parallel sides) × (Distance between them) 

= `1/2 (a + b) h`

(ii) False: For a square inscribed in a circle of radius r the diagonal = diameter = 2r and diagonal = side × `sqrt(2)`.

So, side = `(2r)/sqrt(2) = rsqrt(2)` and area = side² = 2r².

With r = 14, area = 2 × 14² = 392 cm², not 196 cm².