What is the area of the rhombus ABCD below if AC=12 cm and BE= 8 cm?

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Question

What is the area of the rhombus ABCD below if AC=12 cm and BE= 8 cm?

Options:

A . 384 cm²

B . 192 cm²

C . 48 cm²

D . 96 cm²

Answer: Option D
:
D

The diagonals of a rhombus bisect each other. Therefore, in the given figure:

$\Rightarrow B E = D E$

$\Rightarrow B D = 2 \times B E$

$\Rightarrow B D = 2 \times 8 = 16 c m$

Area of a rhombus equals half the product of length of the two diagonals.

$\Rightarrow$ Area of ABCD = $\frac{1}{2} \times A C \times B D$
$⟹$ Area of ABCD= $\frac{1}{2} \times 12 \times 16 = 96 c m^{2}$ .

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