Area of a Rectangle: Using ratios for calculation

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:

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

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

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:

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

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

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:

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

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

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:

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

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

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:

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

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

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:

$8,8\times4=8,32$

First we will divide the area of KBCM by the area of AKMD.

We know that their ratio is 2:1, therefore:

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

We also know the area of AKMD, so we'll substitute it into the formula to obtain the following:

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

Finally, we multiply by 18:

$KBCM=2\times18=36$