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

Solution

## 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 = Product of diagonals2 = 8×62 = 24 cm2 Hence, joining the midpoints of the adjacent sides of the rectangle, we obtain a rhombus of area 24 cm2.

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