Question

name date period workbook activity
chapter 10, lesson 6
area formulas
example find the area of a triangle whose base = 24 cm
and height = 16 cm.
make a sketch, label, and use the formula.
$a=\frac{1}{2}bh$
$a=\frac{1}{2}(24)(16)=\frac{1}{2}(384)=192\\ cm^{2}$
directions find the area in square units.
1.
2.
3.
4.
5.

Explanation:

Step1: Recall the formula for the area of a parallelogram

The formula for the area of a parallelogram is \(A = bh\), where \(b\) is the base and \(h\) is the height. For problem 1, \(b = 15\mathrm{cm}\) and \(h=8\mathrm{cm}\). Then \(A = 15\times8=120\mathrm{cm}^2\).

Step2: Recall the formula for the area of a triangle

The formula for the area of a triangle is \(A=\frac{1}{2}bh\). For problem 2, \(b = 14\mathrm{in}\) and \(h = 6\mathrm{in}\). So \(A=\frac{1}{2}\times14\times6=42\mathrm{in}^2\).

Step3: Recall the formula for the area of a rectangle

The formula for the area of a rectangle is \(A = lw\) (or \(A=bh\)). For problem 3, \(l = 21\mathrm{ft}\) and \(w = 14\mathrm{ft}\). Then \(A=21\times14 = 294\mathrm{ft}^2\).

Step4: Use the triangle - area formula again

For problem 4, \(b = 16\mathrm{in}\) and \(h = 5\mathrm{in}\). Using \(A=\frac{1}{2}bh\), we get \(A=\frac{1}{2}\times16\times5=40\mathrm{in}^2\).

Step5: Recall the formula for the area of a square

The formula for the area of a square is \(A = s^2\) (since \(l = w=s\) for a square). For problem 5, \(s = 13\mathrm{m}\). So \(A=13\times13=169\mathrm{m}^2\).

Answer:

1. \(120\mathrm{cm}^2\)
2. \(42\mathrm{in}^2\)
3. \(294\mathrm{ft}^2\)
4. \(40\mathrm{in}^2\)
5. \(169\mathrm{m}^2\)