An umbrella is made by stitching 10 triangular pieces of cloth of two different colours, each piece measuring 25 cm, 25 cm and 14 cm.How much cloth of each colour is required for the umbrella?
Answers
Answer:
please mark mas the brainliest
Step-by-step explanation:
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