Area of a Rectangle: Using ratios for calculation

The area of a rectangle is 50.

$EB=\frac{1}{5}AB$

$EF\Vert BD$

Work out the area of the rectangle EBFD.

Since AB is 5 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 $\frac{1}{5}$

$S_{\text{ABCD}}=5\times S_{EBFD}$

Let's input the known data into the formula:

$50=5\times S_{\text{EBFD}}$

$S_{\text{EBFD}}=10$

10

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.

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:

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

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

20

The area of a rectangle is 36.

$EB=\frac{1}{6}AB$

$EF\Vert BD$

Calculate the area of rectangle EBFD.

Since AB is 6 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 $\frac{1}{6}$

$S_{\text{ABCD}}=6\times S_{EBFD}$

Let's input the known data into the formula:

$36=6\times S_{\text{EBFD}}$

$S_{\text{EBFD}}=6$

6

The area of the rectangle below is: 16.

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

$EF\Vert BD$

Calculate the area of the rectangle EBFD.

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:

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

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

4

The area of a rectangle is 256 cm².

One side is 4 times longer than the other.

What are the dimensions of the rectangle?

To find the area of the rectangle, we multiply the length by the width.

According to the data in the statement, one side will be equal to X and the other side will be equal to 4X

Now we replace the existing data:

$S=x\times4x$

$256=4x^2$

We divide the two sections by 4:

$64=x^2$

We extract the square root:

$x=\sqrt{64}=8$

If we said that one side is equal to x and the other side is equal to 4x and we know that x=8

From here we can conclude that the sides of the rectangle are equal:

$8,8\times4=8,32$

8 x 32

The area of the rectangle below is equal to 49.

$EB=\frac{1}{7}AB$

$EF\Vert BD$

Calculate the area of the rectangle EBFD.

Since AB is 7 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 $\frac{1}{7}$

$S_{\text{ABCD}}=7\times S_{EBFD}$

Let's input the known data into the formula:

$49=7\times S_{\text{EBFD}}$

$S_{\text{EBFD}}=7$

7

Given the rectangle ABCD that was divided into a small rectangle KBCM and the square AKMD.

It is known that the ratio between the rectangle and the square is 2:1.

Given the area of the square AKMD is 16 cm².

Calculate the area of the rectangle KBCM

We will divide the area of KBCM by the area of AKMD

We are given that the ratio is 2:1, therefore

$\frac{KBCM}{AKMD}=\frac{2}{1}$

We know the area of AKMD, so we'll substitute it and get:

$\frac{KBCM}{18}=\frac{2}{1}$

We'll multiply by 18:

$KBCM=2\times18=36$

32