Question

Math - An umbrella is made by stitching 10 triangular
pieces of two different colours, each piece measuring
20cm, 50cm and 50cm.
Mr. Amit wants to donate 20 such umbrellas to the
children of slum area.

(ii) Find the cloth required for 20 such umbrella. step by step
​

Answer 1

Answer:

2,400cm

Step-by-step explanation:

1 umbrella made up 10 triangular pieces Whose measuring =20cm,50 cm,50 cm sum of these length=120cm

It means that 1 umbrella made up of 120 cm cloth

So 20such umbrella made up of 120×2= 2,400cm .

Answer 2

$\displaystyle\large\underline{\sf\red{Given}}$

✭ There is a umbrella made up of 10 triangular pieces of length 20 cm, 50 cm & 50 cm

✭ Amit is gonna make 20 such umbrellas

$\displaystyle\large\underline{\sf\blue{To \ Find}}$

◈ Length of the cloth required?

$\displaystyle\large\underline{\sf\gray{Solution}}$

So here we may find the area of each triangular pieces, then multiply it with the number of triangles and then with the total number of umbrellas!!

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$\underline{\bigstar\:\textsf{According to the given Question :}}$

So we shall first find the semi perimeter, that is,

›› $\displaystyle\sf Semi \ Perimeter = \dfrac{Perimeter}{2}$

›› $\displaystyle\sf Semi \ Perimeter = \dfrac{20+50+50}{2}$

›› $\displaystyle\sf Semi \ Perimeter = \dfrac{120}{2}$

›› $\displaystyle\sf \purple{Semi \ Perimeter = 60 \ cm}$

So then we shall find the are with the help of the Heron's formula, that is,

$\displaystyle\underline{\boxed{\sf Area = \sqrt{s(s-a)(s-b)(s-c)}}}$

• s = 60
• a = 20
• b = 50
• c = 50

Substituting the values,

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

➝ $\displaystyle\sf \sqrt{60(60-20)(60-50)(60-50)}$

➝ $\displaystyle\sf \sqrt{60\times 40\times10\times 10}$

➝ $\displaystyle\sf \sqrt{240000}$

➝ $\displaystyle\sf \green{489.9 \ cm^2}$

Now for 1 umbrella we use 10 such pieces,so

»» $\displaystyle\sf 489.9 \times 10$

»» $\displaystyle\sf \orange{Per \ Umbrella = 4899 \ cm^2}$

So then for 20 such umbrellas,

➳ $\displaystyle\sf 4899\times 20$

➳ $\displaystyle\sf \pink{97980 \ cm^2}$

$\displaystyle\sf \therefore \:\underline{\sf Cloth \ required \ is \ 97980cm^2}$

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