Question

applying the area of a trapezoid formula
a plot of land has an area of 33 75 square feet. jackson wants to put a 4 - foot by 4 - foot shed on the land. he can only do this if the height of the trapezoid is at least 4 5 feet. what is the height of the trapezoid? feet

Explanation:

Step1: Recall area formula for trapezoid

The formula for the area of a trapezoid is $A=\frac{(b_1 + b_2)h}{2}$, where $b_1$ and $b_2$ are the lengths of the parallel - sides and $h$ is the height. Here, $b_1 = 5$ ft, $b_2=10$ ft, and $A = 33.75$ square feet.

Step2: Substitute values into formula

We substitute the known values into the formula: $33.75=\frac{(5 + 10)h}{2}$.

Step3: Simplify the equation

First, simplify the sum in the parentheses: $33.75=\frac{15h}{2}$.

Step4: Solve for h

Multiply both sides of the equation by 2 to get $33.75\times2 = 15h$, so $67.5=15h$. Then divide both sides by 15: $h=\frac{67.5}{15}=4.5$ feet.

Answer:

$4.5$