Question

Find the area of isosceles triangle ABC in which $AB=AC=5cm$ and $BC=8cm.$

• A. $12c{m}^2$
• B. $14c{m}^2$
• C. $16c{m}^2$
• D. None of the above

Answer 1

Answer: (A)

$12c{m}^2$

The height of the isosceles triangle divides it into two right angled triangles.
$a^2=h^2+{\left(\frac{b}{2}\right)}^2$

$\Rightarrow 5^2=h^2+4^2$
$h^2=25-16=9$

$h=\sqrt{9}=3$ cm
Area of triangle $=\frac{1}{2}\times base\times height=\frac{1}{2}\times 8\times 3=12$ sq cm