Question : The length of each side of a rhombus is 10 cm. If the length of one of its diagonals is 16 cm, then what is the area of the rhombus?
Option 1: 108 cm2
Option 2: 112 cm2
Option 3: 128 cm2
Option 4: 96 cm2
Correct Answer: 96 cm 2
Solution :
The area (A) of a rhombus, $A = \frac{1}{2} \times d_1 \times d_2$ where $d_1$ and $d_2$ are the lengths of the diagonals.
Given: $d_1$ = 16 cm
The length of each side of the rhombus is 10 cm.
Using the Pythagorean theorem,
$⇒\left(\frac{d_2}{2}\right)^2 + \left(\frac{d_1}{2}\right)^2 = \text{side}^2$
Substituting the given values into the formula,
$⇒\left(\frac{d_2}{2}\right)^2 = 10^2 - \left(\frac{16}{2}\right)^2 = 100 - 64 = 36$
$⇒d_2 = 2 \times \sqrt{36} = 12$ cm
The area of the rhombus,
$⇒A = \frac{1}{2} \times 16 \, \text{cm} \times 12 \, \text{cm} = 96 \, \text{cm}^2$
Hence, the correct answer is 96 cm
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