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

Answer 1

To find the total area, we need to calculate the area of each shape in the image and then add them together.

The area of the horizontal rectangle is given by:
Length x Width = 5 cm x 3 cm = 15 cm²

The area of the vertical rectangle is also 15 cm².

The area of the quarter circle can be calculated using the formula:
(1/4) x π x r², where r is the radius of the quarter circle.

Area of quarter circle = (1/4) x 3.14 x 3 cm x 3 cm
= 7.065 cm² (rounded to the nearest hundredth)

Now, we can add up the areas of all three shapes:

Total area = 15 cm² + 15 cm² + 7.065 cm²
≈ 37.07 cm² (rounded to the nearest hundredth)

Therefore, the total area is approximately 37.07 cm².