• # How to find the perimeter and area of ​​a rectangle?

Elena Melnichenko
February 10, 2015

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How to find the perimeter and area of ​​a rectangle?

A rectangle is a geometric figure in which all angles are right and the opposite sides are parallel in pairs.

In order to find the perimeter and area of ​​a rectangle, it is necessary to know several quantities (sides, angle and side, perimeter) and the corresponding formulas. Let's try to understand everything in detail.

## Perimeter rectangle

The perimeter of the figure can be found in several ways, knowing:

• the parties;
• area of ​​the figure and one side;
• diagonal and side.

### Parties

On the two sides, you can easily find the perimeter by the formula: P = a + a + b + b = 2 (a + b), where a and b are the sides of the rectangle. For example, a = 5 cm, b = 7 cm, then the perimeter will be: P = 2 (5 +7) = 24 cm.

For more clarification, see the article How to find the perimeter of a rectangle.

### Square and side

If the problem is given area and one of the parties, then you can easily find the perimeter: a) Find the side, and then the perimeter. S = a * b, that is, one of the parties will be:

• a = S / b, b = S / a.

Perimeter calculated by the above formula.

• P = (2S + 2a2)/ a or P = (2S + 2b2)/ b.

### Diagonal and side

The perimeter can also be found on the known side with the diagonal, using the formula: P = 2 (a + √d2- a2) or P 2 (b + √d2 -b2), where d is the diagonal of the figure.

## Rectangle area

As with the perimeter calculation, you can use the same values.

### Two sides

The area on both sides is calculated as follows: S = a * b.

### Perimeter and side

There are two options for solving such problems:

1. Find the second side by the formula: a = (P - 2b) / 2. And then, knowing the necessary quantities, calculate the area.
2. You can also immediately substitute all values ​​in the formula: S = (Pa - 2a2)/ 2 or S = (Pb - 2b2)/2.

### Diagonal and side

If the task specifies a diagonal and one of the sides, then the area is calculated:

• S = a * √ (d2- a2)or S = b * √ (d2- b2).

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