Contents
Basic definitions
A rectangle is a quadrilateral in which all angles are equal. They are also straight and are 90°.
The perimeter is the sum of the lengths of all sides of the polygon. The generally accepted designation is the capital Latin letter P. Under “P”, it is convenient to write the name of the figure in small letters so as not to get confused in the tasks along the way.
If the lengths of the sides are given in different units, we will not be able to find out the perimeter of the rectangle. Therefore, for the correct solution, it is necessary to convert all data to one unit of measure.
What is the perimeter measured in?
- millimeter (mm);
- centimeter (cm);
- decimeter (dm);
- meter (m);
- kilometer (km) and other units of length.
In this publication, we will consider how to calculate the perimeter of a rectangle and analyze examples of solving problems.
Perimeter Formula
The perimeter (P) of a rectangle is equal to the sum of the lengths of all its sides.
P = a + b + a + b
Because opposite sides of this figure are equal, the formula can be represented as follows:
- Double side: P = 2*(a+b)
- The sum of the double values of the sides: P = 2a+2b
The short side is the height/width of the rectangle, the longer side is its base/length.
Examples of tasks
Task 1
Find the perimeter of a rectangle if its sides are 5 cm and 8 cm.
Decision:
We substitute the known values u2bu5binto the formula and get: P u8d 26 * (XNUMX cm + XNUMX cm) uXNUMXd XNUMX cm.
Task 2
The perimeter of the rectangle is 20 cm, and one of its sides is 4 cm. Find the second side of the figure.
Decision:
As we know, P=2a+2b. Let’s say 4 cm is a side а. So the unknown side b, multiplied by two, is calculated as follows: 2b u2d P – 20a u2d 4 cm – 12 * XNUMX cm uXNUMXd XNUMX cm.
Therefore, side b = 12 cm / 2 = 6 cm.
Problem solving
And now practice!
1. One side of the rectangle is 9cm and the other is 11cm longer. How to find out the perimeter?
How do we decide:
If a = 9, then b = 9 + 11;
Then b = 20 cm;
Let’s use the formula P = 2 × (a + b);
P = 2 × (9 + 20);
Answer: 58 cm.
2. Find the perimeter of a rectangle with sides 30 mm and 4 cm. Express your answer in centimeters.
How do we decide:
Convert 30 mm to cm:
30 mm = 3 cm.
Use the formula for the perimeter of a rectangle:
P \u003d 3 + 4 + 3 + 4 \u003d 14 cm.
Answer: P = 14 cm.
3. Find the perimeter of a triangle with sides 2 in and 300 mm. Express your answer in centimeters.
How do we decide:
Let’s convert the side lengths to centimeters:
2 dm = 20 cm, 300 mm = 30 cm.
Find the perimeter using the formula P = 2 × (a + b):
P \u003d 2 × (20 + 30) \u003d 2 × 50 \u003d 100 (cm).
Answer: P = 100 cm.
