Question : The sides of a rhombus are 10 cm each and the diagonal measures 16 cm. The area of the rhombus is:
Option 1: 96 sq. cm
Option 2: 160 sq. cm
Option 3: 100 sq. cm
Option 4: 40 sq. cm
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Correct Answer: 96 sq. cm
Solution :
Area of rhombus ABCD = 2 × area of $\triangle$ABD
$\therefore$ Semi perimeter of $\triangle$ABD = $\frac{10+10+16}{2}$ = 18 cm
Now, the area of $\triangle$ABD
= $\sqrt{18(18-10)(18-10)(18-16)}$
= $\sqrt{18×8×8×2}$
= $\sqrt{2304}$
= $48$ sq. cm
So, the area of rhombus ABCD = 2 × 48 = 96 sq. cm
Hence, the correct answer is 96 sq. cm.
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