Question

The perimeter of a rhombus is 52 cm and one diagonal is 10 cm long. Then the area of the rhombus is

• A. $260{cm}^2$
• B. $520{cm}^2$
• C. $120{cm}^2$
• D. $240{cm}^2$

Answer 1

The correct option is C $120{cm}^2$

$p=4a=52cm,a=\frac{52}{13}\simeq 13cmBypythagorastheoremOD=\sqrt{{DC}^2-{OC}^2}=\sqrt{{13}^2-5^2}=\sqrt{144}=12cm\therefore DB=2\times 12=24cmAreaofrhombus=\frac{1}{2}{d}_1{d}_2\approx \frac{1}{2}\times 10\times 24=120{cm}^2$'