Question

If an isosceles triangle has a perimeter of $18cm$ and base $8cm$, then its area is ___ .

• A. $45c{m}^2$
• B. $68c{m}^2$
• C. $12c{m}^2$
• D. $20c{m}^2$

Answer 1

The correct option is C

$12c{m}^2$

Let each of its equal sides be x.
Then, $2x+8=18$ $\Rightarrow x=5cm$
Hence, the sides are $\text{5 cm, 5 cm and 8 cm}$.
Using the Heron's formula,
$Area\left(A\right)=\sqrt{s(s-a)(s-b)(s-c)}$
where s = semi- perimeter and a,b,c are the three sides of the triangle.
$Semi-Perimeter\left(s\right)=\frac{\text{perimeter}}{2}$
$=\frac{18}{2}$ $=9cm$
$A=\sqrt{9(9-5)(9-5)(9-8)}$
$=\sqrt{9\times 4\times 4\times 1}$
$=\sqrt{144}c{m}^2$
$=12c{m}^2$