Question

An umbrella made by stitching 10 triangular pieces of cloth of two different colour each pieces measuring 14 m ,13 m and 17m. How much cloth of each colour is required for umbrella.​ Please tell me the answer

Answer 1

QUESTION:-

An umbrella made by stitching 10 triangular pieces of cloth of two different colour each pieces measuring 14 m ,13 m and 17m. How much cloth of each colour is required for umbrella.​

EXPLANATION:-

Area of each cloth=5(Area of 1 triangle)

Area of  1 triangle can be calculated by herons formula i.e.

$\boxed{\bf\;\sqrt{s(s-a)(s-b)(s-c)}}$

Where

s is semi-perimeter

a,b,c are sides

So to find the area first  we have to find the semiperimeter ,

s=(a+b+c)/2

a=14

b=13

c=17

s=(14+13+17)/2

s=44/2

s=22 m

So now we can find area of the triangle

$\sf\;\sqrt{22(22-14)(22-13)(22-17)} \\\\\rightarrow \sqrt{22\times 8\times 9\times 5} \\\\\rightarrow \sqrt{1584\times 5} \\\\\rightarrow \sqrt{7920} \\\\\rightarrow 12\sqrt{55}$

So the area of 1 cloth is 12√55

Area of umbrella=10×12√55

==> 100√55

cloth of each colour is required for umbrella=100√55 m

Answer 2

Answer:

Total cloth required for a colour is 445.02 m² and Total cloth required for different colour is 445.02 m².

Step-by-step explanation:

Given,

Sides of triangular piece of cloth is 14 m, 13m and 17 m.

We know,

Heron's formula :

• Area of triangle = √s(s - a)(s - b)(s - c)

[Where, s is semi-perimeter, a, b and c are sides of triangle]

So,

• Semi-perimeter = Perimeter/2

→ Semi-perimeter = 14 + 13 + 17/2

→ Semi-perimeter = 44/2

→ Semi-perimeter = 22

Semi-perimeter is 22 cm.

Then,

→ Area = √22(22 - 14)(22 - 13)(22 - 17)

→ Area = √22 × 8 × 9 × 5

→ Area = √2 × 11 × 2 × 2 × 2 × 3 × 3 × 5

→ Area = 2 × 2 × 3 × √11 × 5

→ Area = 12√55

→ Area = 12 × 7.417

→ Area = 89.004

Area of triangular piece of cloth is 89.004 m².

• There are 10 triangular pieces of cloth of two different colours means 5 is of a colour and 5 is of another colour.

Now,

Area for 5 pieces of a colour :

→ Area = 5 × 89.004

→ Area = 445.02

Area of 5 pieces of another colour :

→ Area = 5 × 89.004

→ Area = 445.02

Thus,

Total cloth required for a colour is 445.02 m² and Total cloth required for another colour is 445.02 m².