Question

An isosceles triangle has its base of $20$ cm and each of its equal sides is $26$ cm long. Calculate its area

• A. $250$
• B. $240$
• C. $156$
• D. none of the above

Answer 1

The correct option is B $240$

Consider an Isosceles triangle $ABC$, with $AB=AC=26$ cm., $BC=20$ cm
Draw a perpendicular $AD$ on non- congruent side $BC$.
In an Isosceles triangle a perpendicular bisects the non congruent side.
Hence, $BD=\frac{1}{2}BC=\frac{1}{2}\left(20\right)=10$ cm
In $△ABD$,
$\Rightarrow A{B}^2=A{D}^2+B{D}^2$
$\Rightarrow {26}^2=A{D}^2+{10}^2$
$\Rightarrow 676=A{D}^2+100$
$\Rightarrow A{D}^2=576$
$\Rightarrow AD=24$ cm
Area of triangle $=$ $\frac{1}{2}AD\times BC$
$=$ $\frac{1}{2}(24\times 20)$
$=$ $240$ ${\text{cm}}^2$