Use the image to answer the 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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To find the total area, we need to calculate the areas of the two rectangles and the quarter circle, and then add them together.
The area of each rectangle is given by length × width. Since both rectangles have the same dimensions of 5 cm by 3 cm, the area of each rectangle is 5 cm × 3 cm = 15 cm^2.
The area of the quarter circle can be calculated using the formula A = πr^2/4, where A is the area and r is the radius. In this case, the radius is 3 cm, so the area of the quarter circle is (3.14 × 3 cm^2)/4 = 7.065 cm^2.
To find the total area, we add the areas of the two rectangles and the quarter circle: 15 cm^2 + 15 cm^2 + 7.065 cm^2 ≈ 37.07 cm^2.
Therefore, the total area is approximately 37.07 cm^2.