Question

practice & problem solving
leveled practice in 7 - 9, find the area of each figure.
7.
8.
total area = area of parallelogram + area of trapezoid
=7·□ + 1/2·(□ + 5)·□
=□ + 28
=□ft²
the total area is □ square feet.
total area = area of rhombus + area of triangle
=□·□ + 1/2·□·□
=□ + □
=□in.²
the total area is □ square inches.
9.
area of original figure = area of
=□·□
=□yd²
the total area is □ square feet.

1. michelle is laying carpet in her hallway

a. choose efficient methods michelle wants to decompose her hallway into the fewest number of quadrilaterals possible. what shapes will she decompose it into?
b. how many square feet of carpet does michelle need?

Explanation:

Problem 7

Step1: Area of parallelogram

The formula for the area of a parallelogram is \(A = base\times height\). Here, the base of the parallelogram is \(7\) ft and the height is \((6 - 4)=2\) ft. So, \(A_{parallelogram}=7\times2\)

Step2: Area of trapezoid

The formula for the area of a trapezoid is \(A=\frac{1}{2}(a + b)h\), where \(a = 2\) ft, \(b = 5\) ft and \(h = 4\) ft. So, \(A_{trapezoid}=\frac{1}{2}(2 + 5)\times4\)

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Step1: Area of rhombus

The formula for the area of a rhombus (which can be considered as a parallelogram) is \(A = base\times height\). Here, the base is \(14\) in and the height is \(6\) in. So, \(A_{rhombus}=14\times6\)

Step2: Area of triangle

The formula for the area of a triangle is \(A=\frac{1}{2}\times base\times height\). Here, the base is \(14\) in and the height is \(6\) in. So, \(A_{triangle}=\frac{1}{2}\times14\times6\)

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Step1: Recognize the equivalent figure

By moving the shaded parts, the original figure is equivalent to a parallelogram. The base of the parallelogram is \(7\) yd and the height is \(4\) yd.

Step2: Calculate the area

Using the formula \(A = base\times height\), we have \(A=7\times4\)

$$A = 28$$

Answer:

The total area is \(42\) square feet.

Problem 8