Finite Math Examples

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\begin{array}{r} b_{1} = & b \\ b_{2} = & y \\ h = & h \end{array}

$\begin{array}{r} b_{1} = & b \\ b_{2} = & y \\ h = & h \end{array}$

Step 1

The area of a trapezoid is equal to

\frac{1}{2}

$\frac{1}{2}$ times the height times the sum of the bases

b_{1} + b_{2}

$b_{1} + b_{2}$ .

\frac{1}{2} \cdot (h e i g h t) \cdot (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 = h

$h = h$ and bases (

b_{1} = b

$b_{1} = b$ and

b_{2} = y

$b_{2} = y$ ) into the formula for the area of a trapezoid.

\frac{1}{2} h \cdot (b + y)

$\frac{1}{2} h \cdot (b + y)$

Step 3

Combine

\frac{1}{2}

$\frac{1}{2}$ and

h

$h$ .

\frac{h}{2} \cdot (b + y)

$\frac{h}{2} \cdot (b + y)$

Step 4

Apply the distributive property.

\frac{h}{2} b + \frac{h}{2} y

$\frac{h}{2} b + \frac{h}{2} y$

Step 5

Combine

\frac{h}{2}

$\frac{h}{2}$ and

b

$b$ .

\frac{h b}{2} + \frac{h}{2} y

$\frac{h b}{2} + \frac{h}{2} y$

Step 6

Combine

\frac{h}{2}

$\frac{h}{2}$ and

y

$y$ .

\frac{h b}{2} + \frac{h y}{2}

$\frac{h b}{2} + \frac{h y}{2}$