Answer:

Given: Dimensions of each triangular piece used in umbrella.

Reasoning: By using Heron’s formula, we can calculate the area of a triangle.

Heron's formula for the area of a triangle, Area = √s(s - a)(s - b)(s - c)

Where a, b, and c are the sides of the triangle, and

s = Semi-perimeter = Half the Perimeter of the triangle = (a + b + c)/2

We know that umbrella is made of 10 triangular pieces of cloth of two different colours.

Let us calculate the area of one triangle.

For each triangle, a = b = 50 cm, c = 20 cm

Semi Perimeter

s = (a + b + c)/2

= (50 + 50 + 20)/2

= 120/2

= 60 cm

By using Heron’s formula,

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

= √s(s - a)(s - b)(s - c)

= √60(60 - 50)(60 - 50)(60 - 20)

= √60 × 10 × 10 × 40

= 200√6 cm2

Therefore,

Area of 10 triangular pieces = 10 × 200√6 cm2 = 2000√6 cm2

Hence, cloth required for each colour = (Total area of the cloth)/2

= (2000√6)/2

= 1000√6 cm2

Thus, 1000√6 cm2 cloth of each colour is required for the umbrella.

Answer:

[tex]\boxed{\bf\:Area\:of \: cloth \: of \: each \: colour \: is \: 1000 \sqrt{6} \: {cm}^{2} \: } \\ [/tex]

Step-by-step explanation:

Given that, An umbrella is made by stitching 10 triangular pieces of cloth of two different colours as shown in fig, each piece measuring 20 cm, 50 cm and 50 cm.

Let's first evaluate the area of one triangular piece of length 20 cm, 50 cm and 50.cm.

Let assume that a = 20 cm, b = 50 cm, c = 50 cm

Now, Semi-perimeter, s of a triangular piece

[tex]\sf\: s = \dfrac{a + b + c}{2} \\ [/tex]

[tex]\sf\: s = \dfrac{20 + 50 + 50}{2} \\ [/tex]

[tex]\sf\: s = \dfrac{120}{2} \\ [/tex]

[tex]\implies\sf\:s = 60 \: cm \\ [/tex]

Now,

[tex]\sf\: Area\:of\:one\:triangular\:piece \\ [/tex]

[tex]\sf\: = \: \sqrt{s(s - a)(s - b)(s - c)} \\ [/tex]

[tex]\sf\: = \: \sqrt{60(60 - 20)(60 - 50)(60 - 50)} \\ [/tex]

[tex]\sf\: = \: \sqrt{60(40)(10)(10)} \\ [/tex]

[tex]\sf\: = \: 200 \sqrt{6} \: {cm}^{2} \\ [/tex]

Thus,

[tex]\implies\sf\:Area\:of\:one\:triangular\:piece = 200 \sqrt{6} \: {cm}^{2} \\ [/tex]

So,

[tex]\implies\sf\:Area\:of \: 5\:triangular\:piece = 5 \times 200 \sqrt{6} = 1000 \sqrt{6} \: {cm}^{2} \\ [/tex]

Hence,

[tex]\implies\boxed{\bf\:Area\:of \: cloth \: of \: each \: colour \: is \: 1000 \sqrt{6} \: {cm}^{2} \: } \\ [/tex]