The perimeter of a rectangle is equal to \(\displaystyle width+width+length+length\). 

Thus, \(\displaystyle 4+4+4x+4x=40\).

Add like terms:

\(\displaystyle 8+8x=40\)

Subtract 8 from both sides:

\(\displaystyle 8x=32\)

Divide both sides by 8:

\(\displaystyle x=4\)

If the rectangle has one side that is \(\displaystyle 6\), we know that two of them must be that size. Therefore, we know that it looks something like this:

If the perimeter is 30, you know that the following equation holds:

\(\displaystyle 12+2x = 30\)

This means that the other two sides can be found by solving for \(\displaystyle x\):

\(\displaystyle 2x = 30-12\)

\(\displaystyle 2x = 18\)

\(\displaystyle \frac{2x}{2}=\frac{18}{2}\)

\(\displaystyle x=9\)

The area of a rectangle is equal to its base times its height:

\(\displaystyle A = 6*9=54\)

If one side is \(\displaystyle 10\), the doubled side must be \(\displaystyle 20\). Therefore, the rectangle looks like this:

The area of a rectangle is equal to its base times its height:

\(\displaystyle A = BH = 10 * 20 = 200\)

The area of a rectangle is defined as the base multiplied by its height. Therefore, for this rectangle:

\(\displaystyle A=12.4*8.3=102.92\)

Based on what we were told, our rectangle looks like this:

We know, therefore, that there is \(\displaystyle 120-20\) or \(\displaystyle 100\) remaining for the other two sides. This means that they are \(\displaystyle 50\). So, our rectangle ultimately looks like this:

The area of a rectangle is its base times its height. Therefore, the area is:

\(\displaystyle 50 * 10 = 500\)

To find the area of a rectangle apply the formula: 

\(\displaystyle Area= Width\times Length\)

This problem provides the measurements for both the width and length of the rectangle. 

Thus, the solution is: 

\(\displaystyle Area=12\times13=156\)

In this problem you are given the width and perimeter of the rectangle. However, to solve for the area of the rectangle you must first find the length of the rectangle. To do so, work backwards using the formula: 

\(\displaystyle Perimeter=2(W+L)\)

\(\displaystyle 56=2(15+L)\)

\(\displaystyle 56=30+2L\)

\(\displaystyle 2L=56-30=26\)

\(\displaystyle L=\frac{26}{2}=13\)

Now that you know the width and length of the rectangle, apply the area formula: 

\(\displaystyle Area=Width\times Length\)

\(\displaystyle Area=15\times 13= 195\) 

To find the area of a rectangle apply the formula: 

\(\displaystyle Area= Width\times Length\)

The image provides the measurements for both the width and length of the rectangle. 

Thus, the solution is: 

\(\displaystyle Area=20\times9=180\)

Tip for mental math: Since you are multiplying \(\displaystyle 9\) times a multiple of ten, you can think of these factors as:

\(\displaystyle 2\times9=18\) and then tack on one zero to the product because the orginal factors have a total of one zero--which equals a product of \(\displaystyle 180\).

To solve this problem, first note that the width of the rectangle must equal: 

\(\displaystyle 35\times \frac{1}{5}=\frac{35}{5}=7\)

Now that you know the width and length of the rectangle, apply the area formula: 

\(\displaystyle Area=Width\times Length\)

\(\displaystyle Area=35\times 7= 245\) 

To find the area of a rectangle apply the formula: 

\(\displaystyle Area= Width\times Length\)

This problem provides the measurements for both the width and length of the rectangle. 

Thus, the solution is: 

\(\displaystyle Area=26\times23=598mm^2\)