Question

If the side of a rhombus is 6 cm and its one diagonal is 8 cm. Find the area of the rhombus in ${cm}^2$.

• A. $9\sqrt{3}$
• B. $3\sqrt{9}$
• C. $16\sqrt{5}$
• D. $8\sqrt{5}$

Answer 1

The correct option is C

$16\sqrt{5}$

Side of the rhombus = 6 cm

One of the diagonal = 8 cm

Semi perimeter of the triangle containing the diagonal = $\frac{(6+6+8)}{2}$ = 10 cm

Area of the triangle containing the diagonal = $\sqrt{s(s-a)(s-b)(s-c)}$

= $\sqrt{10(10-6)(10-6)(10-8)}$

= $\sqrt{10\times 4\times 4\times 2}$
= $\sqrt{2\times 5\times 4\times 4\times 2}$
$\Rightarrow 8\sqrt{5}c{m}^2$

Area of rhombus = 2 (Area of the triangle containing the diagonal)

Area of the rhombus = $2\times 8\sqrt{5}$ = $16\sqrt{5}$${cm}^2$