Question

#8
listen
find the height of the trapezoid.
area $= 180 \text{ km}^2$
4 km
14 km
the height is $square$ kilometers.

Explanation:

Step1: Recall trapezoid area formula

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

Step2: Substitute given values

We know \( A = 180 \, \text{km}^2 \), \( b_1 = 4 \, \text{km} \), \( b_2 = 14 \, \text{km} \). Substitute these into the formula:
$$180 = \frac{1}{2}(4 + 14)h$$

Step3: Simplify the base sum

Calculate the sum of the bases first:
$$180 = \frac{1}{2}(18)h$$
$$180 = 9h$$

Step4: Solve for height \( h \)

Divide both sides by 9 to isolate \( h \):
$$h = \frac{180}{9}$$

Answer:

20