Question

A hand fan is made by stitching $10$ equal size triangular strips of two different type of paper as shown in figure. The dimensions of equal strips are $25cm,25cm$ and $14cm$. Find the area of each types of paper needed to make the hand fan.

Answer 1

$a=25cm,b=25cm,c=14cm$

$s=\frac{a+b+c}{2}=\frac{25+25+14}{2}=\frac{64}{2}=32cm$

Area of one triangular strip $=\sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)}$

$$\begin{array}{c}=\sqrt{32\left(32-25\right)\left(32-25\right)\left(32-14\right)}\\ =\sqrt{32\times 7\times 7\times 18}\\ =\sqrt{16\times 2\times 7\times 7\times 3\times 3\times 2}\\ =4\times 7\times 3\times 2\\ =168c{m}^2\end{array}$$

Area of each types of paper needed

$\begin{array}{c}=5\times 168\\ =840c{m}^2\end{array}$