The area of a trapezoid is 60 square feet. If the bases of the trapezoid are 8 feet and 12 feet, what is the height?

Question

Aaliyah Anderson · Accepted Answer

The height is 6 feet.

The formula for the area of a trapezoid is #A=((b_1+b_2)h)/2# where #b_1 and b_2# are the bases and #h# is the height. In the problem, the following information is given: #A=60 ft^2#, #b_1=8ft# , #b_2=12ft# Substituting these values into the formula gives... #60=((8+12)h)/2# Multiply both sides by #2#. #2 * 60=((8+12)h)/2 *2 # #120=((20)h)/cancel2 * cancel2# #120=20h# Divide both sides by #20# #120/20=(20h)/20# #6=h# #h=6ft#

Jayden Jackson · Answer

undefined To find the height of the trapezoid, we can use the formula for the area of a trapezoid, which is given by:

$$ \text{Area} = \frac{1}{2} \times (\text{sum of bases}) \times (\text{height}) $$

Given that the area of the trapezoid is 60 square feet and the bases are 8 feet and 12 feet, we can plug these values into the formula and solve for the height:

$$ 60 = \frac{1}{2} \times (8 + 12) \times (\text{height}) $$
$$ 60 = \frac{1}{2} \times 20 \times (\text{height}) $$
$$ 60 = 10 \times (\text{height}) $$

Now, divide both sides by 10 to solve for the height:
$$ \text{height} = \frac{60}{10} $$
$$ \text{height} = 6 \text{ feet} $$

Therefore, the height of the trapezoid is 6 feet.