Table of Contents Part 1: Calculate the area of ??regular polygons using edge-center distance 1. A calculation formula for the area of ??a regular polygon is: area = 1/2x perimeter x edge-center distance. 2. Obtain the edge-center distance of the polygon. 3. Obtain the perimeter of the polygon. 4. Distance between edges and centers. 5. Simplify the answer. Part 2: Use other formulas to calculate the area of ??regular polygons 1. Calculate the area of ??an equilateral triangle. 2. Calculate the area of ??the square. 3. Calculate the area of ??the rectangle. 4. Trapezoidal area formula. Part 3: Calculating the area of ??an irregular polygon 1. Use the coordinates of each vertex of the irregular polygon to calculate its area. 2. Create an array. 3. Multiply the abscissa of each vertex by the ordinate of the next point. 4. Multiply the ordinate of each vertex by the abscissa of its next point. 5. Divide the result of step 36 and the previous step by 2 to get the area of ??the polygon: 120/2=60 square units. You may know how to calculate the area of ??rectangles and triangles, but can you calculate the area of ??more complex polygons? If you know the coordinates of each vertex of a polygon, here is a relatively simple way to calculate its area.
Part 1: Calculate the area of ??a regular polygon using the side-center distance
1. A calculation formula for the area of ??a regular polygon is: area = 1/2x perimeter x side-center distance. The explanation of this formula is as follows: Perimeter: The sum of the lengths of all sides.
Edge-center distance: the vertical distance from the center of the polygon to each side.
2. Obtain the edge-center distance of the polygon. If the question asks you to use the edge-center distance method, generally speaking, the size of the edge-center distance will be given in the question. For example, you want to calculate the area of ??a regular hexagon whose side-center distance is 10√3.
3. Obtain the perimeter of the polygon. If you already know the perimeter, just substitute it into the formula directly. If it is a regular polygon, and the length of the edge-to-center distance is given. Then calculate the perimeter as follows. Think of the side-center distances as the opposite sides of the 60° angle in a right triangle with triangles of 30°, 60°, and 90°. A regular hexagon is composed of six regular triangles, and the side-center distance divides the regular triangle into two right-angled triangles.
In this right triangle, the side opposite 60° is √3 times the side opposite 30°. If the length of the side opposite 60° is 10√3, then the length of the side opposite 30° is x=10.
The x above is the general length of the base of a triangle. Therefore, the length of the base is 20, and 20 times 6 is the perimeter of the regular hexagon, which is 120.
4. Substitute the side-center distance and perimeter into the formula. If you are using the above "area = 1/2x perimeter x side-center distance", substitute accordingly: area = 1/2x120x10√ 3
Area=60x10√3
Area=600√3
5. Simplify the answer. Some questions require you to write the decimal form of your answer. Use a calculator to calculate, √3x600=1,039.2, this is a form of the final answer.
Part 2: Use other formulas to calculate the area of ??regular polygons
1. Calculate the area of ??the equilateral triangle. Use the following formula: area = 1/2x base x height. For example, if the base is 10 and the height is 8, the area is 1/2x8x10, which is 40.
2. Calculate the area of ??the square. As long as you know the length of one side, you can calculate its square. This is the same principle as the formula for the area of ??a rectangle (length x width). If the side length of the square is 6, then the area is 6x6, or 36.
3. Calculate the area of ??the rectangle. Multiply the length by the width to get the area. If the length is 4 and the width is 3, then 4x3=12, which is the area.
4. Trapezoidal area formula. Area = [(upper base length + lower base length) x height]/2. For example, if you have a trapezoid with two bases of 6 and 8 and a height of 10, the area is [(6+8)x10]/2, which can be simplified to (14x10)/2, which is 140/2. Got 70.
Part 3: Calculate the area of ??an irregular polygon
1. Use the coordinates of each vertex of the irregular polygon to calculate its area. If you know the coordinates of each vertex of an irregular polygon, then its area can be found.
2. Create an array. Using the polygon shown in the above figure as a reference, list the abscissa and ordinate of each vertex in a table in counterclockwise order. Please list the coordinates of the first point again at the end of the table, as shown in the figure below:
3. Multiply the abscissa of each vertex by the ordinate of the next point. Add up all the results.
4. Multiply the ordinate of each vertex by the abscissa of its next point. Add these results together.
5. Subtract the final result of step 4 from the final result of step 3, as shown in the figure below: 82-(-38)=120
6. Divide the result of the previous step Taking 2, we get the area of ??the polygon: 120/2=60 square units.
Tips If you list the coordinates of the vertices clockwise instead of counterclockwise, the area you get will be a negative number. So, you can use this method to check that you have listed the vertices of this polygon in the correct way.
This method calculates the area of ??a polygon with a certain direction.
If you want to calculate the area of ??a polygon where two lines intersect, such as a figure-eight, just subtract the area calculated counterclockwise from the area calculated clockwise.