b Note that the shorter sides of the rectangle are not included in the perimeter of the shape.
C
c Multiply the perimeter of the original shape by the linear scale factor. Multiply the area of the original shape by the square of the linear scale factor.
A
a 6128 feet^2
B
b $2387.96
C
cArea: 24 512feet^2
Perimeter: 598 feet
Practice makes perfect
a The dog park can be thought of as a circle with a radius of 30 feet and a rectangle with a length and width of 55 feet and 30 feet, respectively.
By calculating the total area of the two shapes and adding them, we can determine how many square feet of grass we have to order. Area: (55)(60)+ 30^2π≈ 6128 feet^2
b Now we need to determine the perimeter so we can make a fence for the park. Like in Part A, we can view the dog park as a rectangle and a circle. However, the shorter sides of the rectangle should not be included in the perimeter. With this information we can determine the perimeter.
Perimeter: 55+55+ 2(30)π= 110+60πfeet
When we know the total perimeter of the fence we can find the cost of the fence by multiplying the perimeter in feet by the cost per foot.
Cost: (110+60π)8≈$2387.96
c Now we need to increase the dog park's size. We can find the perimeter of the new shape if we multiply the original shape's perimeter by the linear scale factor, which is 2 — since we are doubling the park's size. To find the area, we have to multiply the area of the original shape by the square of the linear scale factor.
