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 cm²

(B) a square of area 25 cm²

(C) a trapezium of area 24 cm²

(D) a rhombus of area 24 cm²

Answer 1

(D) a rhombus of area 24 cm²

Explanation:

According to the question,

Let ABCD be the rectangle.

E is the mid-point of the side AB

F is the mid-point of the side BC

G is the mid-point of the side CD

H is the mid-point of the side DA

The figure obtained by joining the midpoints E, F, G and H is rhombus.

Sides of the rectangle is given,

We know that,

Side of the rectangle AB = diagonal of the rhombus FH = 8cm

Similarly,

Side of the rectangle AD = diagonal of the rhombus EG = 6cm

Then,

Area of the rhombus = ½ × EG × FH

= ½ × 6 × 8

= 24 cm²

Hence, option (D) is the correct answer.