Question

The area of square $ABCD$ is three-fourths the area of parallelogram $EFGH$. The area of parallelogram $EFGH$ is one-third the area of trapezoid $IJKL$. If square $ABCD$ has an area of $125$ square feet, calculate the area of trapezoid $IJKL$, in square feet.

• A. $75$
• B. $225$
• C. $350$
• D. $500$

Answer 1

Answer: (D)

$500$

Given, area of square $ABCD$ is three fourth of area of parallelogram $EFGH$,

And the area of parallelogram $EFGH$ is one-third of the area of trapezoid $IJKL$ and area of square $ABCD$ is $125$.

Let the area of trapezoid $IJKL$ is $x$

Then area of parallelogram $EFGH=$ $\frac{1}{3}x$

And area of square $ABCD=$ $\frac{3}{4}$ area of parallelogram $EFGH=$ $\frac{3}{4}\times \frac{1}{3}x=\frac{1}{4}x$

But area of square $ABCD=125$

$\therefore \frac{1}{4}x=125$

$\Rightarrow x=500$

So, area of trapezoid $IJKL=500$.