Question

An umbrella is made by stitching 12 triangular pieces of cloth. Each piece measures '50 cm' 20 cm. Find the area of cloth used in it.

Answer 1

First side of the triangle, a = 50 cm
Second side of the triangle, b = 20 cm
Third side of the triangle, c = 50 cm
∴ Semiperimeter of the triangle, s = $\frac{a+b+c}{2}=\frac{50+20+50}{2}=60\mathrm{cm}$

Now, using Heron’s formula, we have:

$$\begin{gathered} \mathrm{Area}\mathrm{of}\mathrm{the}\mathrm{triangle}=\sqrt{s(s-a)(s-b)(s-c)} \\ =\sqrt{60(60-50)(60-20)(60-50)} \\ =\sqrt{60\times 10\times 40\times 10} \\ =\sqrt{240000} \\ =200\sqrt{6}{\mathrm{cm}}^2 \end{gathered}$$

∴ Area of 12 such triangles = 12 ×$200\sqrt{6}{\mathrm{cm}}^2=2400\sqrt{6}{\mathrm{cm}}^2$