Question
Use the image to answer the question.
An illustration shows a shape that appears as a square with a semicircle attached on the left side and the top. The side of the square is 2 inches and the diameter of the semicircles is 2 inches. The overlapping lines, which include the top and left side of the square, are marked as dashed lines. Right angle symbols are shown on the top left and bottom right corners of the square.
You are making a card for a friend that looks like a heart shape. Solve for the total area of the shape. Use 3.14 as pi. Round the answer to the nearest hundredth.
(1 point)
Responses
16.56 in.2
16.56 in. squared
10.28 in.2
10.28 in. squared
7.14 in.2
7.14 in. squared
5.57 in.2
To find the total area of the shape, we first need to find the areas of the square and the two semicircles separately, and then subtract the overlapped areas.
Area of the square:
Side length = 2 inches
Area = side length x side length = 2 inches x 2 inches = 4 square inches
Area of one semicircle:
Radius = diameter/2 = 2 inches/2 = 1 inch
Area = (1/2) x π x radius^2 = (1/2) x 3.14 x 1^2 = 1.57 square inches
Total area of both semicircles = 2 x Area of one semicircle = 2 x 1.57 = 3.14 square inches
The overlapped area is the area of a quarter circle:
Radius = diameter/2 = 2 inches/2 = 1 inch
Area = π x radius^2 = 3.14 x 1^2 = 3.14 square inches
Now, find the total area (excluding overlap) = Area of square + Total area of semicircles = 4 + 3.14 = 7.14 square inches
Subtract the overlapped area = Total area - Overlapped area = 7.14 - 3.14 = 4.00 square inches
Therefore, the total area of the shape is 4.00 square inches, rounded to two decimal places is 4.00 in.2.
The closest rounded answer provided is:
7.14 in. squared