Rectangle Area Problem: Finding EBFD When EB=1/4AB and Area=16

Question

The area of the rectangle below is: 16.

$EB=\frac{1}{4}AB$

$EF\Vert BD$

Calculate the area of the rectangle EBFD.

00:11 Let's find the area of rectangle E B F D.

00:15 The areas of the rectangles are proportional to the lengths of their sides.

00:22 Now, substitute the given values, and solve to find the area.

00:30 Great job! That's how we find the area.

Since AB is 4 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 and the larger one is $\frac{1}{4}$

$S_{\text{ABCD}}=4\times S_{EBFD}$

Let's input the known data into the formula:

$16=4\times S_{\text{EBFD}}$

$S_{\text{EBFD}}=4$