Question

an umbrella is made by Siddharth for Poor person by stitching 10 triangular pieces of cloth of two different coloured as shown in the figure given each figure measuring 20 CM 50 cm and 50 cm how much cloth of each colour is required for the umbrella

Answer 1

For pieces of triangle,
a = 20 cm , b = 50 cm , c = 50 cm
.°. s = a + b + c / 2
= 20 + 50 + 50 / 2
= 120 / 2 
= 60 cm
.°. a triangles area = √ s ( s - a ) ( s - b ) ( s - c )
= √ 60 ( 60 - 20 ) ( 60 - 50 ) ( 60 - 50 )
= √ 60 ( 40 ) ( 10 ) ( 10 )
= 200√6 cm²
.°. one colour of five triangles area ,
= 5 ( 200√6 ) cm²
= 1000√6 cm²
so, there are 1000√6 cm² cloth of each colour is required for the umbrella.
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Answer 2

The sides of triangle are consider them as a, b and c
so,
a=20cm
b=50cm
c=50cm
we know that area of triangle is
√(S)(S-a)(S-b)(S-c)
here S is semiperimeter that is
S = (a+b+c)÷2
S = (20 +50 + 50)÷2
S = 120÷2
S = 60
so are of triangle should be
area = √(60)(60-20)(60-50)(60-5
area = √(60)(40)(10)(10)
area = √(240000)
area = 100 √(24)
area = 100×2×√(6)
area = 200√(6)
since there are 10 triangles of two different so there should be 5 triangles of same colour
so the area of particular colour of the section should be
5 × 200√(6)
= 1000√(6)
= 1000 × 2.4495
= 2449.5cm^2
so the area of section of particular colour is 2449.5cm^2

:-)