Question 11 Mark
Find the area of an equilateral triangle having altitude h cm.
Answer
View full question & answer→Altitude of a equilateral triangle, having side a is given by;
$\text{Altitude}=\frac{\sqrt{3}}{2}\text{a}$
Substituting the given value of altitude h cm, we get;
$\text{h}=\frac{\sqrt{3}}{2}\text{a}$
$\text{a}=\frac{2}{\sqrt{3}}\text{h cm}$
Area of a equilateral triangle, say A having each side a cm is given by;
$\text{A}=\frac{\sqrt{3}}{4}\Big(\frac{2}{\sqrt{3}}\text{h cm}\Big)^2$
$\text{A}=\frac{\sqrt{3}}{4}\times\frac{4}{3}\text{h}^2$
$\text{A}=\frac{\text{h}^2}{\sqrt{3}}\text{cm}^2$
$\text{Altitude}=\frac{\sqrt{3}}{2}\text{a}$
Substituting the given value of altitude h cm, we get;
$\text{h}=\frac{\sqrt{3}}{2}\text{a}$
$\text{a}=\frac{2}{\sqrt{3}}\text{h cm}$
Area of a equilateral triangle, say A having each side a cm is given by;
$\text{A}=\frac{\sqrt{3}}{4}\Big(\frac{2}{\sqrt{3}}\text{h cm}\Big)^2$
$\text{A}=\frac{\sqrt{3}}{4}\times\frac{4}{3}\text{h}^2$
$\text{A}=\frac{\text{h}^2}{\sqrt{3}}\text{cm}^2$