Question

exercises: find the area of each rectangle or square. if the length of only one side is given, you may assume the figure is a square with equal sides.
1.) 12 m. 4 m. 2.) 7 m. 3.) 4 ½ in. 6 ½ in.
area = ____________ area = __________ area = ____________
4.) complete the table for the area of rectangles: show work here:
length width area of rectangle
9.5 ft. 6.6 ft.
18 yd. 4.5 yd.
10 cm. 26 cm.
5.) complete the table for the area of squares:
length of a side area of square
1.62 cm.
13 ft.
9 ½ yd.
6.) mr. wilkerson is tiling his kitchen floor. the length of the floor is 3.5 meters, and the width is 5 meters. how many square meters of flooring does mr. wilkerson need to buy?
7.) find the area of the shaded parts.
a.) b.)
total area of shaded region ______ total area of shaded region ______

Explanation:

1.

Step1: Calculate the area of the rectangle

The formula for the area of a rectangle is \(A = l\times w\), where \(l = 12m\) and \(w=4m\).
\(A=12\times4 = 48m^{2}\)

2.

Step1: Calculate the area of the square

The formula for the area of a square is \(A = s\times s\), where \(s = 7m\).
\(A=7\times7=49m^{2}\)

3.

Step1: Convert mixed - numbers to improper fractions

\(4\frac{1}{2}=\frac{4\times2 + 1}{2}=\frac{9}{2}\) and \(6\frac{1}{2}=\frac{6\times2+1}{2}=\frac{13}{2}\)

Step2: Calculate the area of the rectangle

Using \(A = l\times w\), \(A=\frac{9}{2}\times\frac{13}{2}=\frac{117}{4}=29\frac{1}{4}in^{2}\)

4.

First row:

Using \(A = l\times w\) with \(l = 9.5ft\) and \(w = 6.6ft\)
\(A=9.5\times6.6=(9 + 0.5)\times6.6=9\times6.6+0.5\times6.6=59.4 + 3.3=62.7ft^{2}\)

Second row:

With \(l = 18yd\) and \(w = 4.5yd\)
\(A=18\times4.5=(20 - 2)\times4.5=20\times4.5-2\times4.5=90 - 9 = 81yd^{2}\)

Third row:

With \(l = 10cm\) and \(w = 26cm\)
\(A=10\times26 = 260cm^{2}\)

5.

First row:

Using \(A=s^{2}\) with \(s = 1.62cm\)
\(A=(1.62)^{2}=1.62\times1.62=(1 + 0.62)^{2}=1^{2}+2\times1\times0.62+0.62^{2}=1+1.24 + 0.3844=2.6244cm^{2}\)

Second row:

With \(s = 13ft\)
\(A=13^{2}=169ft^{2}\)

Third row:

Convert \(9\frac{1}{2}=\frac{9\times2+1}{2}=\frac{19}{2}\)
Using \(A = s^{2}\), \(A=(\frac{19}{2})^{2}=\frac{361}{4}=90\frac{1}{4}yd^{2}\)

6.

Step1: Calculate the area of the rectangle

Using \(A=l\times w\) with \(l = 3.5m\) and \(w = 5m\)
\(A=3.5\times5=(3 + 0.5)\times5=3\times5+0.5\times5=15 + 2.5=17.5m^{2}\)

7a.

Step1: Calculate the area of the first rectangle

\(A_1=(6)\times(3 + 3)=6\times6 = 36cm^{2}\)

Step2: Calculate the area of the second rectangle

\(A_2=5\times3=15cm^{2}\)

Step3: Calculate the total area

\(A=A_1+A_2=36 + 15=51cm^{2}\)

7b.

Step1: Calculate the length of the shaded part

\(l=5 + 3=8m\)

Step2: Calculate the area of the shaded part

Using \(A=l\times w\) with \(w = 2m\)
\(A=8\times2=16m^{2}\)

Answer:

1. \(48m^{2}\)
2. \(49m^{2}\)
3. \(29\frac{1}{4}in^{2}\)
4. \(62.7ft^{2}\), \(81yd^{2}\), \(260cm^{2}\)
5. \(2.6244cm^{2}\), \(169ft^{2}\), \(90\frac{1}{4}yd^{2}\)
6. \(17.5m^{2}\)

7a. \(51cm^{2}\)
7b. \(16m^{2}\)