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Growing a Garden

Solution

The orange-flower garden belongs to Bridget.
Perimeter = 32 ft
Area = 48 ft²

The red-flower garden belongs to Travis.
Perimeter = 30 ft
Area = 32 ft²

The yellow-flower garden belongs to Jessica.
Perimeter = 28 ft
Area = 48 ft²

The purple-flower garden belongs to Stacey.
Perimeter = 26 ft
Area = 40 ft²

Explanation

Step 1

Find the perimeter of the orange-flower garden.
P = 7 ft + 9 ft + 4 ft + 5 ft + 3 ft + 4 ft = 32 ft
The perimeter of the orange-flower garden is 32 ft.

Find the area of the orange-flower garden.
Separate the figure into a rectangle (4 ft x 9 ft) and a square (3 ft x 4 ft).
Use a formula to find the area of each polygon.
(A = l x w)
4 ft x 9 ft = 36 ft²   3 ft x 4 ft = 12 ft²
Add the areas to find the area of the whole figure.
36 ft² + 12 ft² = 48 ft²
The area of the orange-flower garden is 48 ft².

Step 2

Find the perimeter of the red-flower garden.
P = 5 + 2 + 2 + 4 + 2 + 2 + 5 + 8 = 30 ft
The perimeter of the red-flower garden is 30 ft.

Find the area of the red-flower garden.
Think of the garden as a smaller rectangle (2 ft x 4 ft) cut out of a larger rectangle (5 ft x 8 ft). Subtract the area of the smaller rectangle from the area of the larger rectangle.

5 ft x 8 ft = 40 ft²

-2 ft x 4 ft = 8 ft²

32 ft²

The area of the red-flower garden is 32 ft².

Step 3

Find the perimeter of the yellow-flower garden.
P = 6 ft + 8 ft + 6 ft + 8 ft = 28 ft

Find the area of the yellow-flower garden.
6 ft x 8 ft = 48 ft²
The area of the yellow-flower garden is 48 ft².

Step 4

Find the perimeter of the purple-flower garden.
P = 5 ft + 8 ft + 5 ft + 8 ft = 26 ft

Find the area of the purple-flower garden.
A = 8 ft x 5 ft = 40 ft²

Step 5

Use the clues to find out which garden belongs to which person.