Question

Find the area of an isosceles triangle having the base x cm and one side y cm.

Answer 1

Let us assume triangle ABC be the given isosceles triangle having sides AB = AC and base BC. The area of a triangle ABC, say A having given sides AB and AC equals to y cm and given base BC equals to x cm is given by

Where,

Base = BC = x cm; Height = $\sqrt{y^2-\frac{x^2}{4}}$

$$\begin{gathered} A=\frac{1}{2}\left(Base\times Height\right) \\ =\frac{1}{2}\times x\left(\sqrt{y^2-\frac{x^2}{4}}\right) \\ =\frac{x}{2}\left(\sqrt{y^2-\frac{x^2}{4}}\right) \end{gathered}$$