Use the image to answer the question.

Question

An illustration shows a shape that appears as a horizontal rectangle and a vertical rectangle joined with a quarter circle. The length and width of both of the rectangles is 5 centimeters and 3 centimeters. The radius of the quarter circle is 3 centimeters. The overlapping lines, which include the right side of the top rectangle and the top of the bottom rectangle, are marked as dashed lines. A right angle symbol appears where the top of the bottom rectangle and the right side of the top rectangle meet.

You are designing a portion of your backyard for grass. You come up with the image shown. Solve using 3.14 as pi. What is the total area? Round to the nearest hundredth.

(1 point)
cm2
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Answer 1

To find the total area, we need to calculate the area of the two rectangles and the quarter circle, then subtract the overlapping area.

Area of the top rectangle = length x width = 5 cm x 3 cm = 15 cm²
Area of the bottom rectangle = length x width = 5 cm x 3 cm = 15 cm²

Area of the quarter circle = pi x radius² / 4 = 3.14 x 3 cm x 3 cm / 4 ≈ 7.07 cm²

Now we need to subtract the overlapping area between the rectangles:
Overlapping area = width x width = 3 cm x 3 cm = 9 cm²

Now we can find the total area:
Total area = 15 cm² + 15 cm² + 7.07 cm² - 9 cm² = 28.07 cm²

Therefore, the total area is approximately 28.07 cm².