Question

A rectangle having 10cm and 6cm as its dimension was reconstructed to make a rhombus having the same perimeter as that of the rectangle and 60 degree as one of its angle .The area of the rhombus?

Answer 1

Answer:

The area of the rhombus will be 55.42 cm²

Step-by-step explanation:

Perimeter of the rectangle = 2(10+6) = 32 cm

=> Perimeter of rhombus = 4a = 32

=> a = 32/4 = 8 cm

Let the lengths of the diagonals be p and q

Taking one of the right angled triangle in the rhombus formed by both the diagonal and side,

sin30° = [p/2]/a

=> 1/2 = [p/2]/8

=> p = 8

similarly,

cos30° = [q/2]/a

=> √3/2 = q/16

=> q = 8√3

Hence area of the rhombus,

A = pq/2 = 8 x 8√3/2 = 32√3 = 55.42 cm²

Hence the area of the rhombus will be 55.42 cm²