How to find area and perimeter

Content

Steps
Part 1 of 2: Calculating the Perimeter
Part 2 of 2: Calculating Area
Tips
What do you need

The perimeter is the length of the closed contour of the geometric figure, and the area is the amount of space bounded by this closed contour. Mathematical quantities such as area and perimeter are used in everyday life, in construction and in other fields. For example, to paint walls, you need to know how much paint you need, that is, you need to determine the area of the surface to be painted. Similar calculations are made during the construction of a fence or during similar activities. By calculating the area and perimeter in advance, you will save time and money when buying building materials.

Steps

Part 1 of 2: Calculating the Perimeter

1 Determine the shape of the measured object. Perimeter is the length of a closed contour of a geometric shape, and there are various formulas for calculating the perimeter of shapes of different shapes.Remember that if a shape does not have a closed path, then the perimeter of that shape cannot be calculated.
- Start by finding the perimeter of a rectangle or square (especially if this is your first time doing this). Such figures have the correct shape, which makes it easier to find their perimeter.
2 Take a piece of paper and draw a rectangle on it. You will use this shape to find its perimeter. Make sure the opposite sides of the rectangle are the same length.
3 Measure the width of the rectangle (that is, measure the "short" side of the rectangle). This can be done with a ruler or tape measure. Write down the width value (near the "short" side). For example, the width of the rectangle is 3 cm.
- If you are measuring the perimeter of a small figure, use centimeters as units of measurement, and meters for large objects.
- Remember that the opposite sides of the rectangle are equal, so you only need to measure the length of the two adjacent sides.
4 Measure the length of the rectangle (that is, measure the "long" side of the rectangle). This can be done with a ruler or tape measure. Write down the length (near the "long" side).
- For example, the length of the rectangle is 5 cm.
5 Write down the corresponding values near opposite sides. Remember that a rectangle has 4 sides and the opposite sides of the rectangle are equal. Write down the length and width of the rectangle (5 cm and 3 cm in this example) on opposite sides.
6 Add the values of all sides to calculate the perimeter. That is, in the case of a rectangle, write: length + length + width + width.
- In the given example, the perimeter is: 3 + 3 + 5 + 5 = 16 cm.
- You can also use the following formula: perimeter of the rectangle = 2 * (length + width) (this formula is correct, since there are two pairs of the same sides in a rectangle). In the given example: (5 + 3) * 2 = 8 * 2 = 16 cm.
7 Apply different formulas to different shapes. To calculate the perimeter of a different shape, you need a formula. In real life, to find the perimeter of an object of any shape, simply measure the sides. You can also use the following formulas to calculate the perimeter of standard geometric shapes:
- Square: perimeter = 4 * side.
- Triangle: Perimeter = Side 1 + Side 2 + Side 3.
- Irregular Polygon: The perimeter is the sum of all sides of the polygon.
- Circle: circumference = 2 x π x radius = π x diameter.
  - π is pi (a constant of approximately 3.14). If your calculator has a π key, use it to perform more accurate calculations.
  - The radius is the length of the line segment connecting the center of the circle and any point on that circle. The diameter is the length of the line segment passing through the center of a circle and connecting any two points on that circle.

Part 2 of 2: Calculating Area

1 Find the values of the sides of a given figure or object. For example, draw a rectangle (or use the rectangle you drew in the previous chapter). In the above example, to calculate the area of a rectangle, you need to find its length and width.
- Use a ruler or tape measure to measure the length and width of the rectangle. In this example, we will use the values of the sides of the rectangle from the previous chapter, namely width = 3 cm, length = 5 cm.
2 The essence of the area of a geometric figure. Calculating the area enclosed by a closed loop is like dividing the interior of a shape into 1-unit x 1-unit squares. Keep in mind that the area of a shape can be larger or smaller than the perimeter of that shape.
- You can break the given figure into unit squares (1 cm x 1 cm or 1 m x 1 m) to visualize the process of calculating the area of the figure.
3 Multiply the length and width of the rectangle. In the example given: area = 3 * 5 = 15 square centimeters.Remember that area is measured in square units (square kilometers, square meters, square centimeters, and so on).
- You can write area units as follows:
  - kilometers² / km²
  - meters² / m²
  - centimeters² / cm²
4 Apply different formulas to different shapes. To calculate the area of a shape of another shape, you will need a corresponding formula. You can use the following formulas to calculate the area of standard geometric shapes:
- Parallelogram: area = base x height
- Square: square = side 1 x side 2
- Triangle: area = ½ x base x height
  - In some textbooks, this formula looks like this: S = ½ah.
- Circle: area = π x radius²
  - The radius is the length of the line segment connecting the center of the circle and any point on that circle. The square of the radius is the radius value multiplied by itself.

Tips

The area and perimeter formulas in this article apply to 2D shapes. If you need to find the volume of a three-dimensional shape, such as a cone, cube, cylinder, prism, or pyramid, find the corresponding formula in a textbook or on the Internet.