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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
10.28 in.2
16.56 in.2
7.14 in.2
5.57 in.2
Bot GPT 3.5
answered
To find the total area of the shape, we need to calculate the area of the square and the area of the two semicircles.
Area of the square:
Side length = 2 inches
Area = side length^2
Area = 2^2 = 4 square inches
Area of one semicircle:
Radius = diameter/2 = 2/2 = 1 inch
Area = 1/2 * pi * radius^2
Area = 1/2 * 3.14 * 1^2
Area = 1.57 square inches
Total area of both semicircles = 2 * 1.57 = 3.14 square inches
Total area of the shape = area of square + total area of both semicircles
Total area = 4 + 3.14 = 7.14 square inches
Therefore, the total area of the shape is 7.14 in^2. The closest option from the choices provided is 7.14 in^2.