Question

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

• A. $2400\sqrt{6}$ c$m^2$
• B. $2200\sqrt{3}$ c$m^2$
• C. $1200\sqrt{6}$ c$m^2$
• D. $1000\sqrt{6}$ c$m^2$

Answer 1

The correct option is A $2400\sqrt{6}$ c$m^2$

Given, an umbrella is made of 12 triangular pieces each of measure 50 cm, 20 cm, 50 cm.
To find area of cloth required we have to first find the area of one piece of cloth.
Semi perimeter, s=$=\frac{Sumofsidesoftriangle}{2}=\frac{50+20+50}{2}=60cm$
Using heron's formula, Area of one triangular piece$=\sqrt{s(s-a)(s-b)(s-c)}=\sqrt{60(60-50)(60-20)(60-50)}=\sqrt{60\times 10\times 40\times 10}=200\sqrt{6}{cm}^2$
Area of 12 triangular pieces or area of cloth used$=$ Area of one triangular piece $\times$ 12
$=200\sqrt{6}{cm}^2\times 12=2400\sqrt{6}{cm}^2$