Question

question 5 of 25
if the area of the trapezoid below is 75 square units, what is
the value of x?
(image of trapezoid with dc=8, ab=17, height x, right angle at the foot of the height from d to ab)
a. 3 units
b. 1.5 units
c. 12 units
d. 6 units

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 parallel sides (bases), and \( h \) is the height.
Here, \( b_1 = 8 \), \( b_2 = 17 \), \( h = x \), and \( A = 75 \).

Step2: Substitute Values into Formula

Substitute the known values into the formula:
\( 75=\frac{1}{2}(8 + 17)x \)

Step3: Simplify the Equation

First, simplify the sum inside the parentheses: \( 8 + 17 = 25 \).
The equation becomes \( 75=\frac{1}{2}(25)x \), which simplifies to \( 75 = 12.5x \).

Step4: Solve for \( x \)

Divide both sides of the equation by \( 12.5 \):
\( x=\frac{75}{12.5}=6 \)

Answer:

D. 6 units