Question

1. mr. goddard is going to place a layer of

in his garden. his blueprint shows the garderind
below:
if the blueprint has a scale factor of 1 cm:2.5
feet, then how many square feet of mulch do
mr. goddard need?

Explanation:

Step1: Calculate the area of the trapezoid on the blueprint

The formula for the area of a trapezoid is \(A=\frac{(a + b)h}{2}\), where \(a\) and \(b\) are the lengths of the parallel sides, and \(h\) is the height.
Here, \(a = 5\space cm\), \(b=7\space cm\), \(h = 3\space cm\).

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Step2: Convert the scale factor to area scale factor

Since the scale factor for length is \(1\space cm:2.5\space feet\), the scale factor for area is \((1\space cm)^{2}:(2.5\space feet)^{2}=1:6.25\)

Step3: Calculate the actual area

Let \(A_{actual}\) be the actual area. Using the proportion \(\frac{A_{blueprint}}{A_{actual}}=\frac{1}{6.25}\)

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Answer:

\(112.5\space square\space feet\)