The height of an equilateral triangle is 5√3 cm, then its area is:

The correct answer is Option (4) → \(25\sqrt{3}\) cm²

The height of an equilateral triangle meets the base at its midpoint, at a right angle, so it cuts the triangle into two right triangles. For a side \(a\), Pythagoras gives the height \(\displaystyle \sqrt{a^2-\left(\frac{a}{2}\right)^2}=\frac{\sqrt{3}}{2}a\).

The side (the height is \(5\sqrt{3}\) cm):

• \(\displaystyle \frac{\sqrt{3}}{2}a=5\sqrt{3}\)

• \(a=10\) cm

The area:

• Area \(\displaystyle =\frac{1}{2}\times\text{base}\times\text{height}=\frac{1}{2}\times10\times5\sqrt{3}=25\sqrt{3}\) cm²