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 .

Answer 1

Hint: In order to solve the question , we need to understand the given mathematical statement properly . The trapezoid is a type of quadrilateral having at least one pair of parallel sides which are opposite to each other . We have to calculate here the area of trapezoid IJKL, in square feet . So, we will first consider the area of trapezoid as a variable named ‘ $ x $ ’ . Then we will write the figures as per the given question mentioned with respect to the area by using variable ‘ $ x $ ’ . Thereafter, perform the required calculations to get the desired solution.

Complete step-by-step answer:
To solve the question , the information provided to us are
Area of a square ABCD is three fourth of area of parallelogram EFGH .
Area of parallelogram EFGH is one third of the area of trapezoid IJKL and
Area of square ABCD is $ 125 $ .
Now let's consider the area of trapezoid IJKL to be ‘ $ x $ ’ .
Then the area of parallelogram EFGH would be = $ \dfrac{1}{3}x $ . { Since, Area of parallelogram EFGH is one third of the area of trapezoid IJKL }
Now , Area of a square ABCD = $ \dfrac{3}{4} \times $ Area of parallelogram EFGH
Which becomes ,
$
   \Rightarrow \dfrac{3}{4} \times \dfrac{1}{3}x \\
   \Rightarrow \dfrac{1}{4}x \\
  $ .
So, the area of a square ABCD = $ \dfrac{1}{4}x $
But as we are given the area of square ABCD = $ 125 $ .
So we can compare or equate the two quantities , we get –
 $
   \Rightarrow \dfrac{1}{4}x = 125 \\
   \Rightarrow x = 125 \times 4 \\
   \Rightarrow x = 500 \;
  $
Therefore , the area of trapezoid IJKL = $ x = 500 $ feet.
So, the correct answer is “ $ x = 500 $ feet”.

Note: Always try to understand the mathematical statement carefully and keep things distinct .
Remember the properties and apply appropriately .
Choose the options wisely , it's better to break the question and then solve part by part .
Cross check the answer and always keep the final answer simplified .