Question

The figure obtained by joining the mid-points of the adjacent sides of a rectangle of sides 8 cm and 6 cm is a ________ of area _________.

Answer 1

Given:
A rectangle ABCD of sides 8 cm and 6 cm
i.e., AB = 8 cm and AD = 6 cm
And a quadrilateral PQRS formed by joining the mid-points of the adjacent sides of ABCD.



We can see that QS || AB and PR || AD
Also, QS = AB = 8 cm and PR = AD = 6 cm
Thus, angle between QS and PR is 90°
Therefore, PQRS is a rhombus.

Area of rhombus = $\frac{1}{2}$× SQ × PR
= $\frac{1}{2}$× 8 × 6
= 4 × 6
= 24 cm²

Hence, the figure obtained by joining the mid-points of the adjacent sides of a rectangle of sides 8 cm and 6 cm is a rhombus of area 24 cm².