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, d 1 and d 2 be the side, diagonal 1 and diagonal 2 of the rhombus respectively. side of rhombus (a) = 13 cm diagonal of rhombus (d 1 ) = 24 cm We know that Area of Rhombus = (product of diagonals)/ 2 = (d 1 x d 2 )/2 ……..(1) a 2 = (d 1 /2) 2 + (d 2 /2) 2 ……….(2) Putting all the values in eq. (1) to find d 2 13 2 = (24/2) 2 + (d 2 /2) 2 169 = (12) 2 + (d 2 /2) 2 169 – 144 = (d 2 /2) 2 25 x 4 = (d 2 ) 2 (d 2 ) 2 = 100 d 2 = 10 …..(3) Putting all the values in eq. (1), we get Area of Rhombus = (24 x 10)/2 Area of Rhombus = 120 cm 2 Hence, (B) is the correct answer. Study about Co-ordinate Geometry Formulas and Tricks.