Question

The figure formed by joining the midpoints of the adjacent sides of a rectangle of sides 8 cm and 6 cm is a
(a) rectangle of area 24 cm²
(b) square of area 24 cm²
(c) trapezium of area 24 cm²
(d) rhombus of area 24 cm²

Answer 1

(d) rhombus of 24 cm²

We know that the figure formed by joining the midpoints of the adjacent sides of a rectangle is a rhombus.
So, PQRS is a rhombus and SQ and PR are its diagonals.
i.e., SQ = 8 cm and PR = 6 cm
∴ ar(rhombus PQRS​) = $\frac{1}{2}$ ×​ product of diagonals = $\frac{1}{2}$ ×​ 8 ×​ 6 = 24 cm²