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
7.14 in.2
5.57 in.2
To solve for the total area of the shape, we first need to find the area of the square and the area of the semicircles.
The area of the square is calculated by multiplying the length of one side by itself:
Area of square = (side length)^2 = 2^2 = 4 square inches
The area of the semicircle is half the area of a full circle. The formula for the area of a circle is A = πr^2, where r is the radius (half the diameter). The radius of the semicircle is 2/2 = 1 inch.
Area of semicircle = (1/2) * π * (radius)^2 = (1/2) * 3.14 * 1^2 = 1.57 square inches
Since there are two semicircles, the total area of the semicircles is 2 * 1.57 = 3.14 square inches.
To find the total area, we add the area of the square and the area of the semicircles together:
Total area = Area of square + Area of semicircles
Total area = 4 + 3.14 = 7.14 square inches
Therefore, the total area of the shape is 7.14 in.².