Question

Calculate the area of an equilateral triangle whose height is $20cm$. Find the area of triangle whose sides are $17cm$ , $8cm$ and $15cm$ .

Answer 1

Step 1: Find area of equilateral triangle.

Height of equilateral triangle (h) $=20cm$

And, Area of an equilateral triangle with height (h) $=\frac{h^2}{\sqrt{3}}$

So, Area of equilateral triangle $=\frac{\left(20\times 20\right)}{\sqrt{3}}$

Area of equilateral triangle $=230.930sq.cm$

Step 2: Find area of right triangle.

Given sides of triangle $=17cm$ , $8cm$ and $15cm$

And, according to the Pythagoras theorem

${\left(15\right)}^2+{\left(8\right)}^2={\left(17\right)}^2$

So, given triangle is right angle.

Also, Area of a right triangle (A) $=\frac{1}{2}\times b\times h$

$$\begin{gathered} \Rightarrow A=0.5\times 15\times 8 \\ \Rightarrow A=60sq.cm \end{gathered}$$

Hence , the required area is $60sq.cm$