Question

the area of the trapezoid is 160 square centimeters.
14 cm
10 cm
10 cm
26 cm
what is the trapezoids height, h?
h = centimeters

Explanation:

Step1: Recall trapezoid area formula

The area of a trapezoid is given by $A = \frac{1}{2}(b_1 + b_2)h$, where $b_1, b_2$ are the two parallel sides, and $h$ is the height.

Step2: Substitute known values

We know $A=160$, $b_1=14$, $b_2=26$. Substitute into the formula:
$160 = \frac{1}{2}(14 + 26)h$

Step3: Simplify the bracket

Calculate the sum of the bases:
$14 + 26 = 40$
So $160 = \frac{1}{2} \times 40 \times h$

Step4: Simplify the right-hand side

$\frac{1}{2} \times 40 = 20$, so:
$160 = 20h$

Step5: Solve for h

Divide both sides by 20:
$h = \frac{160}{20}$

Answer:

8 centimeters