How To Calculate Perimeter And Area

We will teach you how to calculate the perimeter and area of ​​geometric figures, which you can apply in everyday situations or with abstract figures.

It is very common to confuse the two concepts: perimeter and area. The perimeter is the length of the outline of a figure, while the area is the measure of what is contained within that figure. For example, if we imagine a square and draw it, we will be making the outline. If we measure that contour we will obtain the perimeter that is measured in cm, dm, m, etc. (units of length). Once we draw it and then color what remains inside the square, we will be talking about the area, which will be calculated with a certain formula and will be measured in cm², dm², m², etc. (units of area).

What is often confusing is that with the same elements (measurement of the sides of a rectangle, for example) the perimeter and the area can be calculated but applying different formulas that imply different mathematical operations.

The formulas are used to calculate perimeters and areas of triangles, quadrilaterals and in general of regular polygons, as well as circles. But there are figures that are not regular and it is necessary to break them down into parts to calculate the area, add or subtract one part from another, that is, we must not only use formulas but a lot of reasoning.

What do you need to calculate the perimeter and area?

• Perimeter and area formulas
• Pencil and paper
• Calculator

Instructions for calculating perimeter and area

1. Calculating perimeters does not necessarily require formulas because whatever the polygon is, regular or not, we will obtain its perimeter by adding the lengths of the sides.
2. For example, if a square has a side of 5 cm, its perimeter will be 5cm + 5cm +5cm +5cm = 20 cm, but since the square has 4 equal sides, of the same size, which we will call L, a formula could be written:
3. Perimeter of the square = L x 4      
4. If we want to calculate the perimeter of a rectangle whose sides are L ₁ and L ₂,  we can do it by adding L ₁ + L ₂ + L ₁ + L ₂, but since we know that the opposite sides have the same measure, we could write the formula:
5. Perimeter of rectangle = L ₁x 2 + L ₂   x 2
6. The trianglecan be equilateral (its three equal sides) so its perimeter can be abbreviated as:
7. Perimeter of the equilateral triangle = L x 3
8. But if it is not equilateral we directly add the measure of the sides:
9. Triangle perimeter = L ₁+ L ₂ + L ₃       
10. The parallelogram also has the opposite sides of the same length, so to calculate its perimeter we will do the same as with the rectangle
11. Parallelogram perimeter = L ₁x 2 + L ₂   x 2
12. To calculate the perimeter of regular polygons such as pentagon (5 equal sides), hexagon (6 equal sides), heptagon (7 equal sides), etc. the number of sides is  multiplied by the measure of the side , suppose that the side is L
13. Perimeter of the pentagon = 5 x L       
14. Perimeter of the hexagon = 6 x L      
15. Perimeter of the heptagon = 7 x L      
16. Octagon perimeter = 8 x L      
17. If the figure is irregularwe can calculate its perimeter by adding all the sides.
18. If we want to calculate the perimeter of the circle we must know the measure of its radius, the radius R is the length from the center of the circle to any point of it or the diameter D (which is twice the radius) We must also remember the number π (Pi) whose approximation is: π = 3.14
19. Circumference perimeter = π x D
20. For example, if a circle has a radius of 15 cm and we want to calculate its perimeter, we will do it as follows:
21. Perimeter= πx D = π x 2 x R =14 x 2x 15 cm = 3.14 x 30 cm = 94.2cm
22. Now we will see the calculation of the areas, that is, the   formulas:
23. Area of ​​the square= L x L = L ²
24. Area of ​​rectangle= L ₁ x L ₂    also called   base x height
25. To calculate the area of ​​the triangleor parallelogram we need to know the height ( h ) which is not the same as the side (sometimes it can coincide). The height of a triangle or a parallelogram is the segment perpendicular to the base and that passes through the vertex opposite to it, as shown in the figure. We also need the measurement of the base.
26. To calculate the area of ​​the circle we only have to multiply the number πx the squared radius
27. Area of ​​the circle= π x R ²
28. For example, the area of ​​the circle of radius = 15 cm will be:
29. A = π x R ²= 3.14 x (15 cm) ² = 3.14 x 225 cm ² = 706.5 cm ²
30. If we want to calculate the area of ​​regular polygons like the pentagon, hexagon, etc. We must break the figure into triangles and know the height of those triangles as well as the measure of the sides that are all equal:
31. Pentagon area: 5 x (L x h)/2
32. Hexagon area: 6 x (L x h)/2
33. Heptagon area: 7 x (L xh)/2
34. Octagon area: 8 x (L x h)/2
35. If a Hexagon has a side of 4 cm and the height of the triangles (also called apothem of the hexagon) is 3.5 cm, its area will be calculated as follows:
36. Area = 6 x (4 cm x 3.5 cm) / 2 = 6 x 14cm ² /2 = 42 cm ²
37. There are calculations of areas that require more work, breaking down a figure into simple figures and then adding the areas by applying the known formulas. You can see it in the whole figure, which is then broken down into a triangle, a rectangle, and half a circle.

Tips for Calculating Perimeter and Area

• You should always be clear about the units and not confuse those of perimeter and area because when you solve a geometry problem and you have to say what perimeter or area a figure has, you must accompany the number with the unit.
• Practice looking around you and you will always find figures: a window, a pool, a painting. Try to imagine the lengths of its sides and mentally calculate its perimeter and area.
• Learn more about math or mathematics here