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. A rectangle of area 24
• B. A square of area 25
• C. A trapezium of area 24
• D. A rhombus of area 24

Answer 1

The correct option is D

A rhombus of area 24

We know that, on joining the midpoints of the adjacent sides of a rectangle, we get a rhombus.

Here, length of the rectangle = 8cm and breadth of the rectangle = 6 cm.

Let E, F, G and H be the mid-points of the sides of rectangle ABCD. Then, EFGH is a rhombus. Then, diagonals of rhombus EFGH are EG and HF. Here, EG = BC = 8 cm and HF = AB = 6 cm.

Therefore, Area of rhombus = $\frac{Productofdiagonals}{2}$

= $8\times \frac{6}{2}$

= 24 $c{m}^2$

Hence, joining the midpoints of the adjacent sides of the rectangle, we obtain a rhombus of area 24 $c{m}^2$.