Question

PLEASE HELP!!!!!!!!!

(Finding Area Using Triangles and Rectangles HC)

A gardener is building a flower garden with a border of mulch around it. A model of the design is shown.

A large rectangle with dimensions of 10.5 feet by 16 feet. A smaller rectangle with dimensions of 5.5 feet by 8 feet inside of the larger one.

Part A: Find the area of the mulch border that surrounds the 5.5 ft by 8 ft flower garden. Show all work.

Part B: If the mulch cost $3.64 per sq ft, how much will the mulch for this project cost? Show all work.

Answer 1

Common Work:

Area of Larger rectangle = length x breadth

= 8 x 5.5 = 44 sq. ft.

Area of Smaller rectangle = length x breadth

= 16 x 10.5 = 168 sq. ft.

A.

Area of Mulch = Area of Larger Rectangle - Area of Smaller Rectangle

= 168 - 44 = 124 sq. ft.

B.

Cost of Mulch per sq. ft. = $3.64

Total Cost of Mulch = $451.36

Answer 2

Part A:

To find the area of the mulch border, we need to subtract the area of the smaller rectangle (flower garden) from the area of the larger rectangle.

The area of the larger rectangle is given by:

Area = length * width = 10.5 ft * 16 ft = 168 sq ft

The area of the smaller rectangle (flower garden) is given by:

Area = length * width = 5.5 ft * 8 ft = 44 sq ft

Therefore, the area of the mulch border is:

Area of mulch border = Area of larger rectangle - Area of smaller rectangle

Area of mulch border = 168 sq ft - 44 sq ft = 124 sq ft

Part B:

To find the cost of the mulch for this project, we need to multiply the area of the mulch border by the cost per square foot.

Cost of mulch = Area of mulch border * Cost per sq ft

Cost of mulch = 124 sq ft * $3.64/sq ft

Multiplying the values gives:

Cost of mulch = $451.36

Therefore, the mulch for this project will cost $451.36.