QUESTION) Correct answer only
An umbrella is made by stitching 10triangular pieces of cloth, sides of each piece measuring 20 cm, 50 cm and 50 cm. (:√=.)(i)What will be the area of cloth required for the umbrella?
Answers
Answer:
Solution:
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.
Step-by-step explanation:
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