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Question

The figure obtained by joining the mid-points of the adjacent sides of a rectangle of sides 8 cm and 6 cm, is_________.



Your Answer
A

A rectangle of area 24

Your Answer
B

A square of area 25

Your Answer
C

A trapezium of area 24

Correct Answer
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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