Question

you want to build a garden in your backyard that fits into an odd shaped space and enclose it with a fence to keep the dogs out. use the image of the space below to answer the following questions.
write final answers to one decimal place.
diagram: l - shaped figure with dimensions 3.1 m, 8.4 m, 4.2 m, 8.3 m
a) area of the garden = □ 33.5 ✗ □ meters ✗
b) fencing required = □ □ select an answer▼
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Explanation:

Part a) Area of the garden

Step1: Divide the shape

We can divide the L - shaped garden into two rectangles. Let's call the first rectangle (the vertical part) with width \(w_1 = 3.1\space m\) and height \(h_1=8.4 - 4.2=4.2\space m\). The second rectangle (the horizontal part) has width \(w_2 = 8.3\space m\) and height \(h_2 = 4.2\space m\).

Step2: Calculate area of first rectangle

The area of a rectangle is given by \(A = w\times h\). For the first rectangle, \(A_1=w_1\times h_1=3.1\times4.2\)
\(A_1 = 13.02\space m^{2}\)

Step3: Calculate area of second rectangle

For the second rectangle, \(A_2=w_2\times h_2 = 8.3\times4.2\)
\(A_2=34.86\space m^{2}\)

Step4: Total area

The total area of the garden \(A = A_1+A_2=13.02 + 34.86=47.88\approx47.9\space m^{2}\) (rounded to one decimal place)

Part b) Fencing required (Perimeter)

Step1: Analyze the perimeter

For an L - shaped figure, we can use the property that the perimeter of a rectilinear figure (a figure made up of rectangles) can be calculated by considering the outer sides. If we "unfold" the L - shape, we can see that the perimeter is equal to the perimeter of a rectangle with length \(l = 8.3\space m\) and height \(h = 8.4\space m\) (because the horizontal and vertical "indentations" are compensated by the opposite sides).

The formula for the perimeter of a rectangle is \(P = 2\times(l + h)\)

Step2: Calculate the perimeter

Substitute \(l = 8.3\space m\) and \(h = 8.4\space m\) into the formula:
\(P=2\times(8.3 + 8.4)=2\times16.7 = 33.4\space m\)

Answer:

s:
a) The area of the garden is \(\boldsymbol{47.9}\space m^{2}\)
b) The fencing required is \(\boldsymbol{33.4}\space m\)