Examples with solutions for Area of a Rectangle: Calculate The Missing Side based on the formula

Exercise #1

The area of the rectangle below is equal to 55.

AC = 5.5

Calculate the length of side AB.

555555AAABBBDDDCCC5.5

Video Solution

Step-by-Step Solution

The area of the rectangle is equal to the length multiplied by the width.

Let's input the known data into the formula:

S=AB×AC S=AB\times AC

55=AB×5.5 55=AB\times5.5

Let's divide both sides by 5.5:

AB=10 AB=10

Answer

10

Exercise #2

The area of the rectangle below is equal to 44.

AC = 4

Calculate AB.

444444444AAABBBDDDCCC

Video Solution

Step-by-Step Solution

The area of the rectangle is equal to the length multiplied by the width.

Let's substitute the known data into the formula:

S=AB×AC S=AB\times AC

44=AB×4 44=AB\times4

Let's divide both sides by 4:

AB=11 AB=11

Answer

11

Exercise #3

The area of the rectangle below is equal to 84.

AC = 7

What is the length of side AB?

848484777AAABBBDDDCCC

Video Solution

Step-by-Step Solution

The area of the rectangle is equal to the length multiplied by the width.

Let's input the known data into the formula:

S=AB×AC S=AB\times AC

84=AB×7 84=AB\times7

Let's divide both sides by 7:

AB=12 AB=12

Answer

12

Exercise #4

Below is the rectangle ABCD, which has an area of 30 cm².

S=30S=30S=30555AAABBBCCCDDD

Side AB is equal to 5 cm.
What is the length of side BC?

Video Solution

Step-by-Step Solution

First, we'll multiply side AB by side BC

We are given that side BC equals 5, therefore:

AB×BC=AB×5 AB\times BC=AB\times5

We'll call side AB as X

And therefore:

5x=30 5x=30

We'll divide both sides by 5 and get:

x=6 x=6

Therefore, BC=6 BC=6

Answer

6 cm

Exercise #5

The area of the rectangle below is equal to 24.

AC = 3

What is the length of side AB?

242424333AAABBBDDDCCC

Video Solution

Step-by-Step Solution

The area of the rectangle is equal to the length multiplied by the width.

Let's input the known data into the formula:

S=AB×AC S=AB\times AC

24=AB×3 24=AB\times3

Let's divide both sides by 3:

AB=8 AB=8

Answer

8

Exercise #6

The area of the rectangle below is equal to 63.

AC = 7

How long is side AB?

777AAABBBDDDCCC63

Video Solution

Step-by-Step Solution

We use the formula to calculate a rectangle: length times width:

AB×AC=S AB\times AC=S

We place the existing data into the formula:

AB×7=63 AB\times7=63

7AB=63 7AB=63

We divide both sides by 7:

AB=9 AB=9

Answer

9

Exercise #7

The area of the rectangle below is equal to 27.

AC = 3

Calculate AB.

272727333AAABBBDDDCCC

Video Solution

Step-by-Step Solution

The area of the rectangle is equal to the length multiplied by the width.

Let's put the known data into the formula:

S=AB×AC S=AB\times AC

27=AB×3 27=AB\times3

Let's divide both sides by 3:

AB=9 AB=9

Answer

9

Exercise #8

The area of the rectangle below is equal to 50.

AC = 5

How long is side AB?

505050555AAABBBDDDCCC

Video Solution

Step-by-Step Solution

The area of the rectangle is equal to the length multiplied by the width.

Let's input the known data into the formula:

S=AB×AC S=AB\times AC

50=AB×5 50=AB\times5

Let's divide both sides by 5:

AB=10 AB=10

Answer

10

Exercise #9

The area of the rectangle is equal to 75.

AC = 7.5

Calculate AB.

AAABBBDDDCCC7.575

Video Solution

Step-by-Step Solution

The area of the rectangle is equal to the length multiplied by the width.

Let's input the known data into the formula:

S=AB×AC S=AB\times AC

75=AB×7.5 75=AB\times7.5

Let's divide both sides by 7.5:

AB=10 AB=10

Answer

10

Exercise #10

The area of the rectangle below is equal to 132.

AC = 8.5

Calculate length of side AB.

AAABBBDDDCCC8.5132

Video Solution

Step-by-Step Solution

The area of the rectangle is equal to the length multiplied by the width.

Let's substitute the known data into the formula:

S=AB×AC S=AB\times AC

132=AB×8.5 132=AB\times8.5

Let's divide both sides by 8.5:

AB=15 AB=15

Answer

15

Exercise #11

Below is the rectangle ABCD.

It has an area of 42 cm² and side AD is equal to 12 cm.

What is the length of side DC?
S=42S=42S=42121212AAABBBCCCDDD

Video Solution

Step-by-Step Solution

Remember that to calculate the area of the rectangle, we multiply the length by the width.

Therefore:

42=12×CD 42=12\times CD

42=12CD 42=12CD

Divide both sides by 12:

3.5=CD 3.5=CD

Answer

3.5

Exercise #12

The area of the rectangle below is equal to 15.

AC = 2.5

Calculate AB.

151515AAABBBDDDCCC2.5

Video Solution

Step-by-Step Solution

The area of the rectangle is equal to the length multiplied by the width.

Let's input the known data into the formula:

S=AB×AC S=AB\times AC

15=AB×2.5 15=AB\times2.5

Let's divide both sides by 2.5:

AB=6 AB=6

Answer

6

Exercise #13

The height of the house in the drawing is 12x+9 12x+9

its width x+2y x+2y

Given the ceiling height is half the height of the square section.

Express the area of the house shape in the drawing band x and and.

Video Solution

Answer

3x2+8xy+112x+4y2+3y 3x^2+8xy+1\frac{1}{2}x+4y^2+3y