Question

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

Answer 1

Area of 1 Triangular piece of cloth

s= 50+20+50/2=60.

By using Heron's formula.

Area = √s(s-a)×(s-b)(s-c)

=√60(60-50)(60-20)(60-50)

=√60×10×40×10

=√30×2×5×2×2×20×5×2

=√2×3×5×2×2×5×2×2×2×5×5×2

= 200√6 cm².

Therefore, area of cloth used

= 200√6 × 12  

             

( multiplying by 12 as there are 12 pieces )

                                       

( 200√6 is the area of one piece )

=> Area = 5878.77cm²

Answer 2

Given: An umbrella is made up by stitching 12 triangular pieces of cloth, each measuring 50cm,×20cm×50cm.

( √6=2.45 )

To find: Area of the cloth used in it.

Solution:

S = 50+20+50/2

= 120/2

= 60 cm

Area = √{60 (60-50) (60-20) (60-50)}

= √(60×10×40×10)

= √(20×3×10×20×2×10)

= 20×10 √(3×2)

= 200 √6

= 200 × 2.45 [since, √6=2.45]

= 490 cm²

Area of the cloth used in the umbrella

= (490×12) cm²

= 5880 cm²