Question

4-17 while mrs. poppington was visiting the historic battleground at gettysburg, she talked with the landscapers who were replacing the sod in a park near the visitor center. the part of the lawn being replaced is shown in the diagram. measurements are in yards. the diagram is not drawn to scale, but all corners are right angles.
a. use your ruler to make a scale drawing of the lawn that is being replaced.
let \\(\frac{1}{4}\\) inch equal 1 yard.
b. how many square yards of sod will be needed?
square yards = ______
c. at $2.43 a square yard, how much will the sod cost?
cost of sod = ______

Explanation:

Step1: Calculate the area of the composite figure

The figure can be divided into two rectangles.

• First rectangle: length \(l_1 = 10 + 3+4=17\) yards, width \(w_1 = 6-(6 - 4)=4\) yards. Area \(A_1=17\times4 = 68\) square yards.
• Second rectangle: length \(l_2=3\) yards, width \(w_2=(6 - 4)=2\) yards. Area \(A_2 = 3\times2=6\) square yards.
• Total area \(A=A_1+A_2\)

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Step2: Calculate the cost of the sod

If the cost per square yard is \(C_p=\$2.43\) and the area \(A = 74\) square yards.
The total cost \(C\) is given by \(C = C_p\times A\)

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Answer:

b. Square Yards \(= 74\)
c. Cost of Sod \(=\$179.82\)