Question

landscaping: a landscape company has designed and is installing a garden for a customer. the dimensions of the garden are 25 ft. x 25 ft. the pathway is 3 ft. wide and the circle in the middle has a diameter of 9 feet. here is a picture of the actual garden: how much area of dirt will the client have to plant her garden? round your answer to the nearest tenth. 484.4 ft² 450.5 ft²

Explanation:

Step1: Calculate area of the square garden

The area of a square is $A = s^2$, where $s = 25$ ft. So $A_{garden}=25\times25 = 625$ ft².

Step2: Calculate area of the pathway

The pathway consists of two rectangles along the sides and four corner - squares.
The two rectangles along the sides have dimensions $25\times3$ each, and the four corner - squares have dimensions $3\times3$ each.
The area of the two rectangles is $2\times(25\times3)=150$ ft².
The area of the four corner - squares is $4\times(3\times3)=36$ ft².
The total area of the pathway is $A_{pathway}=150 + 36=186$ ft².

Step3: Calculate area of the circular part

The diameter of the circle is $d = 9$ ft, so the radius $r=\frac{d}{2}=\frac{9}{2}=4.5$ ft.
The area of a circle is $A=\pi r^2$, so $A_{circle}=\pi\times(4.5)^2=\pi\times20.25\approx 3.14\times20.25 = 63.585$ ft².

Step4: Calculate area of dirt

The area of dirt is $A = A_{garden}-A_{pathway}-A_{circle}$.
$A=625-186 - 63.585=375.415\approx375.4$ ft².

Answer:

$375.4$ ft²