# What is the perimeter and area

The perimeter is a geometric term that is often found in the problems. To understand what is the perimeter you want to draw an arbitrary polygon and arm with a ruler. In Greek language the term means «measure around».

## How to calculate the perimeter

The perimeter is denoted by a Latin letter **P**. It can be measured in centimeters, millimeters, meters, or decimeters. To find the perimeter, we need to measure the length of all sides of the polygon. The obtained values need to be folded. The final sum will be the answer to the question: «What is the perimeter of the polygon».

The perimeter is the length of the lines which limit a closed shape (square, rectangle, triangle, etc.).

For example, you can see the polygon with sides 10, 12, 13, and 11 cm Make of the above numbers (10+12+13+11) and get a sum of 46. This is the perimeter of the polygon.

For convenience, the calculation of perimeter in geometry there are a number of formulas. Each formula corresponds to a certain figure.

## Perimeter and area of a square

This is the sum of its four sides. As we know, all sides of a square are the same size. Therefore, we can find the perimeter of a square by multiplying the length of its four sides:

**P= a*4**

**P= a+a+a+a**

For example, we have a square of side 10 cm.

*P= 10*4*

*P=40*

*Answer: 40 cm*

*P**= 10+10+10+10*

*P**=40*

*Answer: 40 cm*

To understand what perimeter and area, you should realize that computes the perimeter length of a shape’s outline, and the area – size of its entire surface.

To find the area of a square, you must use a simple formula:

**S= a*a**

**S=a ^{2}**

**S – square a – square side.**

For example, in the requirements specification States that the length of a side of a square is equal to 10cm.

*S=10*10*

*S= 100**cm ^{2}*

*Answer: 10**0**cm ^{2}*

## Perimeter and area of a rectangle

Side of the rectangle located opposite each other and have the same length, called the opposite. These are length and width, they are conventionally referred to as the Latin letters a and b. The formula for calculating perimeter of rectangle looks like this:

**P= (a+b)*2**

Using this formula, we first find the sum of the width and length and then multiply it by two.

For example, we have a rectangle that has length 6 cm and width 2 cm.

*P**= (6+2) * 2*

*P**= 16*

*Answer: 16 cm*

To find the area of a rectangle, it is necessary to multiply the length by the width. The formula looks like this:

**S= a*b**

For example, in terms of the problem says that the rectangle has length 5 cm and width 2 cm. Changing the letters a and b to the specified number.

*S**= 5*2*

*S**=10 cm ^{2}*

*Answer: 10 cm ^{2}*

## The perimeter of the circle (the circumference)

Each circle has a center. Distance from center of circle to any point lying on the circle is called the radius of the circle. Often students confuse the concept of «circle» and «circle» and trying to determine the area of a circle. This is a serious error. You should separate in my head the concept of «circle» and «circle». The circle is not and cannot be the square, she only has length.

To find the perimeter of a circle, calculate the length of its circumference. There is a formula for finding the circumference of a circle:

**L = 2nr**

**L= 2πd**

**L** – length of circle

**π** is the number PI mathematical constant. It is equal to the ratio of the circumference to the length of its diameter. The ancient name of «PI» — rudolfova number. This number is irrational, its decimal representation after the point never ends.

**π = ****3.141 592 653 589 793 238 462 643 383 279 502**

For convenience of calculations typically use the value 3.14

**R** is the radius of the circle

**D** – diameter of a circle

So, to define the perimeter of the circle, we need to find the product of the radius and 2π. If the task specified diameter,

For example, we have a circle with a radius of 3 cm. Find its perimeter.

*L**= 2*3,14*3*

*L**=6**π*

*L=6*3.14*

*L** = 18.84 cm*

*P*_{K}*= of 18.84 cm*

*Answer: 18.84 cm*

## The difference of the perimeter of the square

Area is the size of the surface of the figure, and the perimeter is the sum of its borders.

Area is always measured in square units (cm^{2}, m^{2}, mm^{2}). Perimeter is measured in units of length – centimeters, millimeters, meters, decimeters.