Question

Please help! The following three shapes are based only on squares, semicircles, and quarter circles. Find the perimeter and the area of each shaded part.

Answer 1

Answer:

perimeter = (18 +9π) cm

area = (81 -20.25π) cm^2

Step-by-step explanation:

The perimeter of the shaded area is the circumference of the circle added to two sides of the square. The circumference of the circle is π times the diameter, so the perimeter is ...

p = 2(9 cm) + π(9 cm) = (18 +9π) cm

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The area of the shaded portion is the difference between the area of the square and the area of the circle. The area of the square is the square of the diameter. The area of the circle is π/4 times that value.

A = (9 cm^2) + (π/4)(9 cm^2) = (81 +20.25π) cm^2

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Comment on circle area

The formula you often see is ...

A = πr^2 . . . . r is the radius

since r = d/2, where d is the diameter, this can also be written as ...

A = π(d/2)^2 = (π/4)d^2

Here, the diameter of the circle is the same as the side length of its enclosing square, so the area of the circle is π/4 times the area of the enclosing square.