In the following figure, O is the centre of a circular arc and AOB is a straight line. Find the perimeter and the area of the shaded region correct to one decimal place. (Take π = 3.142)
Answers
Answer:
The Perimeter of a Shaded region is 59.4 cm and area of the shaded region is 61.1 cm².
Step-by-step explanation:
Given :
∆ACB is a right-angled triangle, in which AC = 12 cm , BC = 16 cm , ∠C = 90°
In right-angled ∆ACB, by using Pythagoras theorem
AB² = AC² + BC²
AB² = 12² + 16²
AB² = 144 + 256
AB² = 40
AB = √400
AB = 20 cm
Diameter of a semicircle = 20 cm
Radius of semicircle, r = 20/2 = 10 cm
Radius of semicircle, r = 10 cm
Perimeter of a Shaded region, P = circumference of semicircle + AC + AB
P = πr + 12 + 16
P = 3.142 × 10 + 28
P = 31.42 + 28
P = 59.42 cm
Perimeter of a Shaded region = 59.4 cm
Area of the shaded region , A = Area of a semicircle - Area of a right angle triangle
A = ½ πr² - ½ × base × height
A = ½ × 3.142 × 10² - ½ × AC × BC
A = ½ × 3.142 × 100 - ½ × 12 × 16
A = 3.142 × 50 - 6 × 16
A = 157.1 - 96
A = 61.1 cm²
Area of the shaded region = 61.1 cm²
Hence, the Perimeter of a Shaded region is 59.4 cm and area of the shaded region is 61.1 cm².
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Step-by-step explanation:
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