Please answer the attached question (q23)!!!
Answers
Answer:
49 ( 2√3 - π ) / 8 cm²
≈ 1.975 cm² (approx)
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Step-by-step explanation:
Join the centres of the circles. This makes an equilateral triangle with side 2×3.5 = 7 cm. The height of this triangle is then
√( 7² + 3.5² ) = 7√3 / 2 cm
The area of this triangle is
1/2 × base × height = 1/2 × 7 cm × 7√3 / 2 cm = 49√3 / 4 cm²
Now look at the sector of one of the circles that is inside this triangle. Since the angle in an equilateral triangle is 60°, this sector is 60/360 = 1/6 of the circle. So the three sectors from the three circles combine to be equal to 1/2 the area of one circle.
That is, the parts of the circles inside the equilateral triangle have area
= 1/2 the area of one circle
= 1/2 × π r² = 1/2 × π × (7/2)² cm² = 49π / 8 cm²
The shaded area is then
= area of triangle formed by centres - area of circles in triangle
= 49√3 / 4 cm² - 49π / 8 cm²
= 49 ( 2√3 - π ) / 8 cm²
≈ 1.975 cm²