Question

Question 3
The figure obtained by joining the midpoints of the adjacent sides of a rectangle of sides 8 cm and 6 cm, is:

A) A rectangle of area $24c{m}^2$
B) A square of area $25c{m}^2$
C) A trapezium of area $24c{m}^2$
D) A rhombus of area $24c{m}^2$

Answer 1

The answer is D.
On joining the mid-points of the adjacent sides of a rectangle, we get a rhombus.

Here, length of rectangle ABCD = 8 cm and breadth of rectangle ABCD = 6 cm.
Let E, F, G and H are the mid-points of the sides of rectangle ABCD,
EFGH is a rhombus.
Then, diagonal of rhombus EFGH are EG and HF.
Here, EG = BC = 8 cm
And HF = AB = 6c m
$\therefore$ Area of rhombus = $\frac{Productofdiagonals}{2}$
$\frac{8\times 6}{2}=4\times 6=24c{m}^2$
Hence, joining the mid-points of the adjacent sides of rectangle forms a rhombus of area $24c{m}^2$.