An umbrella is made by stitching 12 pieces of triangular cloths. If the measure of each piece of cloth is 42cm, 42cm, and 21cm, how much cloth is required to make the umbrella? If per square meter the cost of the cloth is Rs. 1250, find the cost of cloth required to make the umbrella.

Given,

In an umbrella, 

No. of triangular pieces of cloth = 12

Length of each of two equal sides of triangular pieces (a) = 42cm = 42m/100 = 0.42m

and the length of third side (b) = 21cm = 21/100 = 0.21

and the cost of per sq. meter of cloth (C) = Rs. 1250

To find: (I) Total area of cloth

   (ii) Total cost of cloth

By formula,

Area of each isoceles triangle piece of cloth = \(\frac b4\sqrt{4a^2-b^2}\)

= \(\frac{0.21m}4\times\sqrt{4\times(0.42m)^2-(0.21m)^2}\)

= 0.0525m x \(\sqrt{0.7056m^2-0.0441m^2}\)

= 0.0525m x \(\sqrt{0.6615m^2}\)

= 0.0525m x 0.8133m

= 0.0427m² 

Total area of cloth (A) = Area of each piece x No. of pieces cloth

= 0.0427m² x 12

= 0.5124m² 

Now,

The total cost of cloth (T) = Cost of per sq. meter of cloth x area

= Rs. 1250 x 0.5124

= Rs. 640.50

Total area of cloth (A) = 0.5124m² 

and total cost of cloth (T) = Rs.640.50