How to find the perimeter and area of a rectangle?
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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.
The perimeter of the figure can be found in several ways, knowing:
- the parties;
- area of the figure and one side;
- diagonal and side.
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.
As with the perimeter calculation, you can use the same values.
The area on both sides is calculated as follows: S = a * b.
Perimeter and side
There are two options for solving such problems:
- Find the second side by the formula: a = (P - 2b) / 2. And then, knowing the necessary quantities, calculate the area.
- 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).