MATH SOLVE

4 months ago

Q:
# Find the perimeter and area of this figureit is made up of semicircles and quarter circlesplease use the actual symbol pi, do not simplify

Accepted Solution

A:

Answer: A = (16π -32) in² P = (4π +8√2) inStep-by-step explanation:The area is that of a quarter-circle of radius 8 inches less half the area of a square with side length 8 inches. Two formulas are useful: area of a circle = πr² . . . . .r = radius area of a square = s² . . . . s = side lengthThen your area is ... A = (1/4)π(8 in)² - (1/2)(8 in)² = (64 in²)(π/4 -1/2) A = (16π -32) in²____The applicable formulas for the side lengths of your figure are ... arc BD = (1/4)(2πr) = π(r/2) = π(8 in)/2 = 4π in segment BD = (8 in)√2The perimeter is the sum of these lengths, so is ... P = (4π +8√2) in_____Of course, you are very familiar with the fact that an isosceles right triangle with side lengths 1 has a hypotenuse of length √(1²+1²) = √2. Scaling the triangle by a factor of 8 inches means the segment AB will be 8√2 inches long.