in the given figure, ACB is a semicircle whose radius is 10.5 cm and C is a point on the semicircle at a distance of 7 cm from B. find the area of the shaded region
Answers
Answer:
104.16 cm^3
Step-by-step explanation:
Given in the given figure, ACB is a semicircle whose radius is 10.5 cm and C is a point on the semicircle at a distance of 7 cm from B. find the area of the shaded region.
By pythagoras theorem we have,
AB^2 = BC^2 + AC^2
(20)^2 = 7^2 + AC^2
AC = √392
AC = 14√2 cm This will be height.
So area of shaded region = area of semi circle - area of triangle
= 1/2 π r^2 - 1/2 b h
= 1/2 x 22/7 x 10.5 x 10.5 - 1/2 x 7 x 14√2
= 1/2 (346.5 - 98(1.414))
= 207.928/2
So area = 104 cm^2
Thank you for asking this question. Here is your answer:
Area of shaded region = Semicircle area - ΔArea
= 1/2 x πr² - 1/2 x b x h
r = 10.5
b = 7
In ABC right angled Δ at C
AB² = BC² + AC²
(21)² = (7)² + AC²
21² - 7² + AC²
441 - 49 = AC²
√392 = AC
14 √2 cm = AC = h
= 1/2 [πr² - b x h]
= 1/2 [22/7 x 10.5 x 10.5 - 7 x 14√2]
= 1/2 [2425.5/7 - 9852
= 1/2 [346.5 - 98 x1.41]
= 1/2 [346.5 - 138.18]
= 1/2 x 208.32
= 104.16 cm²
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