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