Circles Problem Solving

This figure shows two semicircles connected perfectly to a rectangle along their diameters.

What is the approximate area of the figure? Use 3.14 for pi.

• 117.2 ft²

• 136.5 ft²

• 142.0 ft²

• 251.9 ft²

Answer explanation

If the diameter of the semicircles is 7 ft, then the radius is 3.5 ft.

Since there are two semicircles, you can put them together and find the area of a single circle with a radius of 3.5 ft. Use the formula A = π r².

Add the circle area to the rectangle area for the final answer.

A circular flower garden has a diameter of 16 ft. A square pond is placed in the center that measures 5 feet on each side. About how much of the garden remains for planting flowers? Use 3.14 for pi.

• 75 ft²

• 176 ft²

• 226 ft²

• 779 ft²

Answer explanation

You essentially need to find two areas and subtract them to solve this problem.

Circle area - square area = answer

Be careful while calculating the circle area, as the formula is A = π r², and they gave you the diameter of 16 ft.

The square has sides of 5 ft, so use those to find the square area.

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CCSS.7.G.B.4

The diagram below shows the remodeling of Sam's backyard patio. He has removed two congruent semicircle sections for flower gardens. The diameter of each of the semicircle sections is 2 meters. What is the approximate area of the patio now? Use 3.14 for pi.

• 50 m²

• 54 m²

• 57 m²

• 60 m²

Answer explanation

This problem is essentially a subtraction problem. If you combine the two semi-circles, you can find their area as just one circle with A = π r². Be careful, as you need to use the radius of the circle, not the given diameter of 2 m.

Rectangle area - circle area = answer

The diagram shows a section of the playground that has been marked off in a triangle as a dance area for the school carnival. The center circle will be a special spotlight area with a diameter of 8 feet. What is the approximate area of the shaded portion? Use 3.14 for pi.

• 27 square feet

• 178 square feet

• 228 square feet

• 405 square feet

Answer explanation

This is essentially a subtraction problem. Take the triangle area and subtract the circle area.

Be careful to remember that triangle area is $A\ =\ \frac{1}{2}bh$ and to remember to use the radius of the circle when calculating the circle area with A = π r².

The given diameter is 8 feet.

This is a drawing of Lane's swimming pool. The pool is rectangular with a semi-circular end.
What is the approximate area of Lane's pool? Use 3.14 for pi.

• 1,000 m²

• 1,628 m²

• 2,256 m²

• 3,512 m²

Answer explanation

First of all, you can split the image into the rectangle and semicircle. That should show you that the 25 m is only the rectangle length, not a part of the semicircle. If the diameter of the semicircle is 40 m, the radius is 20 m.

The formula for the area off a semicircle is $A\ =\ \frac{1}{2}\pi\ r^2$ . Find the area of the semicircle.

Now, add to that area the area of the rectangle.

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CCSS.HSG.C.A.2

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CCSS.HSG.C.A.2

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CCSS.HSG.C.A.2

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