Question

An umbrella is made by stitching 10 triangular pieces of cloth of two different colours , each piece measuring 20 cm,50 cm and 50 cm. How much cloth of each colour is required for the umbrella? ​

Answer 1

$1000\sqrt{6} cm^{2}$

Step-by-step explanation:

Given -

• An umbrella is made by stitching 10 triangular pieces of cloth of two different colors , each piece measuring 20 cm,50 cm and 50 cm.  

To find -

• Amount of  cloth of each color is required for the umbrella.

Solution -

• To find the area of the triangle we will need to use heron's formula , and for that we'll have to follow two steps ,

Step 1 - Calculate "s" (half of the triangle's perimeter) :

$s=\frac{a+b+c}{2}$

where , a , b , and c are the sides of the triangle.

Step 2 - Calculate the Area by using heron's formula :

$Area = \sqrt{s(s-a)(s-b)(s-c)}$

where , a , b , and c are the sides of the triangle.

Now , let's solve the question by following these steps :–

$\large s = \frac{20+50+50}{2}$

$⇒ \large s = \Large\frac{\cancel{120}}{\cancel{2}}$

$⇒ \large s = 60$

$Area=\sqrt{60(60-50)(60-50)(60-20)}$

$⇒Area =\sqrt{60(10)(10)(40)}$

$⇒Area =10 × 10× 2\sqrt{6)}$

$⇒Area = 200\sqrt{30} cm^{2}$

This is the cloth required for one triangular piece .

Area of each cloth (of different colors) is ,

$⇒5 × area \: \: of \:\: triangle$

$⇒5 × 200\sqrt{6} cm^{2}$

$⇒\bf \underline \green{1000\sqrt{6} cm^{2} }$

Answer 2

Given:-

In a triangular piece,

• Let a=20cm
• Let b=50cm
• Let c=50cm

To find:-

Amount of cloth of each color is required for the umbrella.

Solution:-

Now,

$\rm \: s = \frac{1}{2}(a + b + c) = \frac{1}{2}(20 + 50 + 50)$

$\rm \: \: \:= \frac{1}{2} \times 120cm = 60cm$

$\rm \: s - a = (60 - 20)cm = 40cm$

$\rm \: s - b = (60 - 20)cm =10cm$

$\rm \: s - c = (60 - 50)cm = 10cm$

∴Area of one triangular piece

$\space \rm \: = \sqrt{s(s - a)(s - b)(s - c)} \\ \\ \space \rm \: = \sqrt{60 \times 40 \times 10 \times 10 {cm}^{2} = 200 \sqrt{6} {cm}^{2} }$

∴Area of 5 red triangles =1000√6 cm^2.

and,area of 5 green triangles=1000√6cm^2