Determine area and perimeter

Content

To step
Part 1 of 2: Determining the circumference
Part 2 of 2: Determining area
Tips
Necessities

The circumference is the length of the entire outer boundary of a flat (two-dimensional) figure, and the area is the measure of its size. Area and perimeter are extremely useful measurements that can be used in household projects, construction, DIY projects, and in estimating the amount of materials you may need. For example, if you want to paint a room, you will need to know how much paint you need or, in other words, how much surface can cover the paint. The same can be said when decorating a yard, building a fence, or doing various other chores at home. In these situations, you can use area and perimeter to save time and money when purchasing materials.

To step

Part 1 of 2: Determining the circumference

Determine the shape you want to measure. The outline is the outer boundary around a closed geometric figure, and different shapes will require different approaches. If the shape you want to find the outline of is not a closed shape, the outline cannot be determined.
- If this is your first time calculating the perimeter, try a rectangle or square. These regular shapes make it easier to determine the outline.
Draw a rectangle on a piece of paper. You use this rectangle as a practice shape and determine its outline. Make sure the opposite sides of your rectangle are the same length.
Determine the length of one side of your rectangle. You can do this with a ruler, tape measure or by making up your own example. Write this number on the side that represents it so you don't forget the length. Imagine that the length of one side of your rectangle is 3 cm.
- Centimeters can be used for small shapes, while meters or kilometers are more suitable for larger circumferences.
- When the opposite sides of rectangles are equal, you only need to measure one of the opposite sides.
Determine the width of one side of your rectangle. You can measure the width with a ruler, tape measure or by making your own sample. Write the value for your width next to the horizontal side of your rectangle it represents.
- Continue with the example: imagine that in addition to a length of 3 cm, the width of your rectangle is 5 cm.
Write the correct measurements on the opposite sides of your rectangle. Rectangles have four sides, but the length of the opposite sides will be the same. This also applies to the width of your rectangle. Write the length and width used in the example (3 and 5 cm, respectively) on the opposite sides of your rectangle.
Add all sides together. Write the following below the sample you created or wrote down: length + length + width + width.
- So in this example, you calculate 3 + 3 + 5 + 5 = 16 (the circumference).
- You can also use the formula 2x (length + width) for rectangles, since the length and width of the opposite sides are equal and therefore doubled. In our example this is: 2 x 8 = 16.
Adjust your approach for different shapes. Unfortunately, different shapes will require different formulas for the outline. In real-life examples, you can measure the outer boundary of any closed geometric shape to determine its perimeter. But you can also use the following formulas to find the outline of other common shapes:
- Square: Length of each side x 4
- Triangle: add all sides together
- Irregular Polygon: Add all sides together
- Circle: 2 x π x radius or π x diameter.
  - The π symbol stands for Pi (pronounced pie). If you have a π key on your calculator, you can use it to be more accurate when using this formula. If not, you can round the value of π to 3.14.
  - The term 'radius' refers to the distance between the center of a circle and its outer boundary (circumference), while 'diameter' refers to the length of an imaginary line between two opposite points on the circumference of a circle passing through the center of the circle. circle goes.

Part 2 of 2: Determining area

Determine the dimensions of your shape. Draw a rectangle or use the same rectangle you drew when determining the outline. In this example, you calculate the area of a rectangle, using its height and width.
- You can work with a ruler or tape measure, or come up with your own example. In this example, the length and width are the same as the previous example used to find the circumference: 3 and 5, respectively.
Understand the true meaning of the surface. Finding the area within an outline is like dividing that empty space inside your shape into 1 by 1 squares. The area can be smaller or larger than the outline, depending on the shape.
- You can divide the shape into vertical and horizontal segments of one unit (cm, m) if you want to visualize what the area measurement will look like.
Multiply the length of your rectangle by the width. In the example: area = 3 x 5, which is 15 square meters. The unit of measure for the area should always be written in square units (square km, square meters, etc.).
- You can write "square units / units squared" as:
  - cm²
  - m²
  - km²
Change your formula depending on the shape. Unfortunately, different geometric shapes will require a different approach to calculate the area. You can use the following formulas to find the area of some common shapes:
- Parallelogram: base x height
- Square: side 1 x side 2
- Triangle: ½ x base x height.
  - Some mathematicians use the notation: A = ½bh.
- Circle: π x r² (where r = radius)
  - The term "radius" refers to the distance between the center of a circle and its outer boundary (circumference), and the small two in superscript (the square) indicates that the value that the two belongs to is multiplied by itself.

Tips

These area and perimeter formulas only work for the area (volume) of a flat shape. If you need to find the contents of a three-dimensional shape (the volume), you have to look for formulas for volume, such as those for cones, cubes, cylinders, prisms, and pyramids.