Question

big ideas math
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find the height of the trapezoid.
area $= 600$ yd$^2$
25 yd
23 yd
the height is $square$ yards.

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 \( b_1, b_2 \) are the two parallel bases, and \( h \) is the height.

Step2: Substitute known values

We know \( A = 600 \, \text{yd}^2 \), \( b_1 = 25 \, \text{yd} \), \( b_2 = 23 \, \text{yd} \). Substitute into the formula:
$$600 = \frac{1}{2}(25 + 23)h$$

Step3: Simplify the base sum

Calculate the sum of the bases:
$$25 + 23 = 48$$
So the equation becomes:
$$600 = \frac{1}{2}(48)h$$
$$600 = 24h$$

Step4: Solve for height \( h \)

Divide both sides by 24 to isolate \( h \):
$$h = \frac{600}{24}$$
$$h = 25$$

Answer:

25