Pre-Algebra Examples

 $\begin{array}{r} b_{1} = & 11 \\ b_{2} = & \frac{1}{2} \\ h = & 7 \end{array}$

Step 1

The area of a trapezoid is equal to $\frac{1}{2}$ times the height times the sum of the bases $b_{1} + b_{2}$ .

$\frac{1}{2} \cdot (h e i g h t) \cdot (b_{1} + b_{2})$

Step 2

Substitute the values of the height $h = 7$ and bases ( $b_{1} = 11$ and $b_{2} = \frac{1}{2}$ ) into the formula for the area of a trapezoid.

$\frac{1}{2} \cdot 7 \cdot (11 + \frac{1}{2})$

Step 3

Combine $\frac{1}{2}$ and $7$ .

$\frac{7}{2} \cdot (11 + \frac{1}{2})$

Step 4

To write $11$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{7}{2} \cdot (11 \cdot \frac{2}{2} + \frac{1}{2})$

Step 5

Combine $11$ and $\frac{2}{2}$ .

$\frac{7}{2} \cdot (\frac{11 \cdot 2}{2} + \frac{1}{2})$

Step 6

Combine the numerators over the common denominator.

$\frac{7}{2} \cdot \frac{11 \cdot 2 + 1}{2}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply $11$ by $2$ .

$\frac{7}{2} \cdot \frac{22 + 1}{2}$

Step 7.2

Add $22$ and $1$ .

$\frac{7}{2} \cdot \frac{23}{2}$

Step 8

Multiply $\frac{7}{2} \cdot \frac{23}{2}$ .

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Step 8.1

Multiply $\frac{7}{2}$ by $\frac{23}{2}$ .

$\frac{7 \cdot 23}{2 \cdot 2}$

Step 8.2

Multiply $7$ by $23$ .

$\frac{161}{2 \cdot 2}$

Step 8.3

Multiply $2$ by $2$ .

$\frac{161}{4}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{161}{4}$

Decimal Form:

$40.25$

Mixed Number Form:

$40 \frac{1}{4}$