Length of one side of a rhombus is 13 cm and one of the diagonal is 24 cm. What is the area (in cm^2) of the rhombus?

A. 60

B. 120

C. 300

D. 240

SSC CGL 2020 13 August 2021 Shift 1

Solution:

Given that:

Let a, d1 and d2 be the side, diagonal 1 and diagonal 2 of the rhombus respectively.

side of rhombus (a) = 13 cm

diagonal of rhombus (d1) = 24 cm

We know that

Area of Rhombus = (product of diagonals)/ 2 = (d1 x d2)/2 ……..(1)

a2 = (d1/2)2 + (d2/2)2 ……….(2)

Putting all the values in eq. (1) to find d2

132 = (24/2)2 + (d2/2)2

169 = (12)2 + (d2/2)2

169 – 144 = (d2/2)2

25 x 4 = (d2)2

(d2)2 = 100

d2 = 10 …..(3)

Putting all the values in eq. (1), we get

Area of Rhombus = (24 x 10)/2

Area of Rhombus = 120 cm2

Hence, (B) is the correct answer.

Study about Co-ordinate Geometry Formulas and Tricks.



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