The figure is made from part of a circle and part of a square.
one width is 2 and one is 5. one length is 2 and one is 5
a. What is the perimeter of this figure, to the nearest
foot?
b. What is the area of this figure, to the nearest
square foot?
To provide an accurate answer, I need to make some assumptions about the shape based on the given dimensions:
1. The two widths and lengths mentioned correspond to the sides of the square and the diameter of the semi-circle that comprises the figure.
2. The figure consists of a semi-circle attached to a square where the diameter of the semi-circle is equal to one of the sides of the square.
Given the widths and lengths are both 2 ft and 5 ft, we can conclude the side of the square is 5 ft (which will match with the diameter of the semi-circle), and the '2' mentioned twice seems to be an extraneous or redundant dimension based on the information given.
Let's calculate the perimeter and area with this interpretation:
a. The Perimeter:
- The perimeter of the square is 4 times the side, but since we have a semi-circle, we will not count one side of the square.
- The perimeter of the removed side of the square is replaced by the circumference of the semi-circle.
Therefore, the perimeter of the square part = 3 sides = 3 x 5 ft = 15 ft.
The perimeter of the semi-circle part is half the circumference of a full circle plus the diameter (which is not included in the previous calculation because it was the removed side of the square). The circumference of a full circle is πd, where d is the diameter. So for the semi-circle, it would be (πd)/2.
The circumference of the semi-circle = (π * 5 ft) / 2 = (π * 2.5 ft).
Adding the perimeter parts together:
Perimeter = 15 ft (square part) + π * 2.5 ft (semi-circle part).
Since π is approximately 3.14159, this gives us:
Perimeter = 15 ft + (3.14159 * 2.5 ft) = 15 ft + 7.854 ft ≈ 22.854 ft.
To the nearest foot, the perimeter is approximately 23 ft.
b. The Area:
- The area of the square part is side^2.
- The area of the semi-circle part is half the area of a full circle with a radius of r = d/2.
Area of the square = 5 ft * 5 ft = 25 ft².
The area of a full circle is πr², so for a semi-circle, it would be (πr²)/2, with r being half of the diameter (5 ft/2 = 2.5 ft).
Area of the semi-circle = (π * (2.5 ft)²) / 2 = (π * 6.25 ft²) / 2 = π * 3.125 ft².
Since π is approximately 3.14159:
Area of the semi-circle ≈ 3.14159 * 3.125 ft² ≈ 9.82 ft².
Total area is the sum of both areas:
Total area = 25 ft² (square part) + 9.82 ft² (semi-circle part) ≈ 34.82 ft².
To the nearest square foot, the area is approximately 35 ft².