Rectangle Area Problem: Finding Smaller Section When EB=1/3AB and EF∥BD

Question

The area of the rectangle below is equal to 60.

$EB=\frac{1}{3}AB$

$EF\Vert BD$

Calculate the area of the smaller rectangle.

00:00 Find the area of rectangle EBFD

00:03 The ratio of areas between the rectangles equals the ratio of sides

00:13 Let's substitute appropriate values according to the given data and solve for the area

00:20 And this is the solution to the question

Since AB is 3 times larger than EB, the area of rectangle EBDF will be smaller than the area of rectangle ABCD accordingly

In other words, the ratio between the smaller rectangle to the larger one is $\frac{1}{3}$

$S_{\text{ABCD}}=3\times S_{EBFD}$

Let's input the known data into the formula:

$60=3\times S_{\text{EBFD}}$

$S_{\text{EBFD}}=20$