Determine the square centimeters (also written "cm2") of any two-dimensional surface is usually a fairly straightforward process. In the simplest cases, when the surface in question is in the shape of a square or rectangle, its area in square centimeters is given by the equation width × length. The area of other plane figures (circles, triangles, etc.) can be calculated using a series of specific mathematical equations. You can also do simple conversions from inches or square feet to square centimeters, if necessary.
Method 1 of 3: Determine the Square Centimeters of a Square or Rectangle
Step 1. Determine the length of the surface to be measured
Squares and rectangles have four straight sides. For rectangles, opposite sides are the same length, while for squares, all sides are equal. Measure either side of the square or rectangle to find the value of the length.
Step 2. Determine the width of the surface to be measured
Next, measure whichever side is in contact with the side whose length you just found. This side should meet the first side at a 90 degree angle. This second measurement is the width of the square or rectangle.
Since all the sides of a square are equal, the resulting measurement for its length will be the same as its width. In this case, you only need to measure one side
Step 3. Multiply length × width
Simply multiply the length and width measurements to determine the area of the square or rectangular surface in square centimeters.
For example, suppose you measure a rectangular surface of length equal to 4 centimeters and width equal to 3 centimeters. In this case, the area of the rectangle is 4 × 3 = 12 square centimeters.
- In the case of squares, since their four sides are equal, you will only have to get the measure of one side and multiply it by itself (a process that is also known as "squaring" or "raising to the second power") to find the value of the area in square centimeters.
Method 2 of 3: Determine the Square Centimeters of Other Figures
Step 1. Find the area of a circle with the equation "area = pi × r2".
To calculate the area of a circle in square centimeters, you only need to know the distance from the center of the circle to the contour given in square centimeters. This distance is called the "radius." Once you have found this value, you just have to enter it in the place of the "r" in the previous equation. Multiply it by itself and then by the mathematical constant "pi" (3, 1415926…) to determine how many square centimeters the surface of the circle measures.
Therefore, a circle whose radius measures 4 centimeters will have an area of 50.27 square centimeters, since this is the product of the multiplication 3.14 × 16
Step 2. Find the area of a triangle with the equation "area = 1/2 b × h"
The area of a triangle in square centimeters is calculated by multiplying its base ("b") by its height ("h"), with both measurements expressed in centimeters. The base of a triangle is simply the length of one of its sides, while its height is the distance from the base side to the opposite vertex, measured by a segment perpendicular to the first. The area of a triangle can be calculated using the measurements of the base and the height corresponding to any of its sides and the opposite vertex.
Therefore, if you choose a base side of length equal to 4 centimeters and its corresponding height is 3 centimeters, the result will be: 2 × 3 = 6 square centimeters
Step 3. Find the area of a parallelogram with the equation "area = b × h"
Parallelograms are similar to rectangles, except that their corners do not have to form 90 degree angles. The proper way to find the area of a parallelogram in square centimeters is similar to how to find the area of a rectangle. You just have to multiply one base of the parallelogram by its height, with both measurements given in centimeters. Its base is the length of one of its sides, while its height is the distance from the opposite side to the first side, measured at right angles.
That is, if the length of a given side is 5 centimeters and its corresponding height is 4 centimeters, the resulting area will be: 5 × 4 = 20 square centimeters
Step 4. Find the area of a trapezoid with the equation "area = 1/2 × h × (B + b)"
A trapezoid is a four-sided figure with one pair of sides parallel to each other and another pair of sides not parallel to each other. To calculate its area in square centimeters, you will take three measurements (in centimeters): the length of the longest parallel side ("B"), the length of the shortest parallel side ("b"), and the height of the trapezoid ("h "), which is the distance measured at right angles between the two parallel sides. Add the lengths of the two sides, multiply the result by the height, and then divide the result in half to find the area of the trapezoid in square centimeters.
Therefore, if the longest side of the trapezoid is 6 centimeters, the shortest side is 4 centimeters, and its height is 5 centimeters, the result is: ½ × 5 × (6 + 4) = 25 square centimeters
Step 5. Find the area of a hexagon with the equation "area = ½ × P × a"
This formula works with any regular hexagon, which is a plane figure with six equal sides and six equal angles. P represents the perimeter, equivalent to the length of a side multiplied by 6 (6 × s) in the case of a regular hexagon. a represents the apothem, which is the length from the center of the hexagon to the midpoint of any of its sides (that is, halfway between any two contiguous vertices). Do this multiplication and record the result to determine the area.
Therefore, if the hexagon has 6 equal sides of 4 centimeters each (which is summarized in "P = 6 × 4 = 24") and its apothem is 3.5 centimeters, the operation to find the area is: ½ × 24 × 3.5 = 42 square centimeters
Step 6. Find the area of an octagon with the equation "area = 2a² × (1 + √2)"
In the case of a regular octagon (with eight equal sides and eight equal angles), you only need to know the length of one side ("a" in the formula) to determine its area. Enter that value in the formula and it will give you the result.
Therefore, if the length of the side of the regular octagon is 4 centimeters, the operation will be: 2 (16) × (1 + 1, 4) = 32 × 2.4 = 76.8 square centimeters
Method 3 of 3: Convert to Square Centimeters
Step 1. Convert the measurements to centimeters before doing the operations
To get the final result in square centimeters, it is easier to use all the measurements required for the formula (such as length, height, and apothem) in centimeters. Therefore, if each side of the square is 1 foot, you will need to convert this measurement to 30.48 cm before calculating the area. Here are a few conversion factors for the most common units of measure:
- 1 foot = 30, 48 cm
- 1 yard = 91, 44 cm
- 1 inch = 2.54 cm
- 1 meter = 100 cm
- 1 millimeter = 0.1 cm
Step 2. Multiply by 929.03 to convert square feet to square centimeters
1 square foot is literally 1 foot squared (or, in other words, 1 foot by 1 foot). This means that it is equal to 30.48 centimeters multiplied by 30.48 centimeters, or 929.03 centimeters. So if you have an area given in square feet, you just have to multiply it by 929.03 to determine the value in square centimeters.
For example, 400 square feet = 400 x 929, 03 = 371 612
Step 3. Multiply by 6.45 to convert square inches to square centimeters
1 inch is roughly equal to 2.54 centimeters, and 2.54 squared (2.54 x 2.54) is equal to 6.45. So if you have to convert a result of 250 inches, multiply 250 by 6.45 to give you 1612.5 square centimeters.