Question

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

Answer 1

In the figure, a hand fan has 5 isosceles and triangle. with sides 25 cm, 25 cm and 14 cm each.

Now area of one triangle,
$s=\frac{a+b+c}{2}=\frac{25+25+14}{2}=\frac{64}{2}=32$
$\therefore$ Area = $\sqrt{s(s-a)(s-b)(s-c)}$
= $\sqrt{32(32-25)(32-25)(32-14)}$
= $\sqrt{32\times 7\times 7\times 18}$
= $\sqrt{4\times 4\times 2\times 7\times 7\times 2\times 3\times 3}$
= $4\times 2\times 3\times 7=168c{m}^2$
$\therefore$ Total area of the fan = $5\times 168=840c{m}^2$