Question

An umbrella is made by stitching 12 triangular pieces of cloth, each measuring $(50cm\times 20cm\times 50cm.)$ Find the area of the cloth used in it.

Answer 1

Let a = 50 cm, b = 20 cm and c = 50 cm

Now,

S = $\frac{a+b+c}{2}$

S = $\frac{50+20+50}{2}$ = $\frac{120}{2}$ = 60 cm

Therefore, area of triangular piece of cloth =$\sqrt{s(s-a)(s-b)(s-c)}$

= $\sqrt{60(60-50)(60-20)(60-50)}$

= $\sqrt{60\times 10\times 40\times 10}$

= 10×10×2√6

= 200√6 = 200 x 2.45 = 490$c{m}^2$

Therefore, the area of one piece of cloth = 490 $c{m}^2$

Now, the area of 12 pieces = 12 x 490$c{m}^2$ = 5880 $c{m}^2$