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?

Explanation:

Step1: Divide the figure into rectangles

The given figure can be divided into three rectangles.

Step2: Calculate the area of each rectangle

• For the first rectangle with length \(l = 10\) yards and width \(w=6\) yards, the area \(A_1=l\times w=10\times6 = 60\) square yards.
• For the second rectangle with length \(l = 3\) yards and width \(w=(6 - 4)=2\) yards, the area \(A_2=l\times w=3\times2=6\) square yards.
• For the third rectangle with length \(l = 4\) yards and width \(w = 4\) yards, the area \(A_3=l\times w=4\times4 = 16\) square yards.

Step3: Calculate the total area

The total area \(A=A_1+A_2+A_3\).

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Answer:

\(82\) square yards.