Question

ABCD is a quadrilateral, with AB parallel to CD (see figure). Point E is between C and D such that AE represents the height of ABCD, and E is the midpoint of CD. If AB is 4 inches long, AE is 5 inches long, and the area of triangle AED is 12.5 square inches, what is the area of ABCD ? (Note: figure not drawn to scale.)

• A. $25i{n}^2$
• B. $30i{n}^2$
• C. $45i{n}^2$
• D. $35i{n}^2$

Answer 1

Answer: (D)

$35i{n}^2$

If E is the midpoint of C, then $CE=DE=x$. You can determine the length of x by using what you know about the area of triangle AED:

$A=\frac{b\times h}{2}$

$12.5=\frac{5x}{2}$

$25=5x$

$\to x=5$

Therefore, the length of CD is 2x, or 10.

To find the area of the trapezoid, use the formula:

$A=\frac{b_1+b_2}{2}\times h$

$=\frac{4+10}{2}\times 5$

$=35i{n}^2$