Q&A for How to Calculate the Area of a Polygon

Divide the polygon into several triangles. Then, calculate the area of each triangle by multiplying the base by half of the height. Add the different areas together to find the total area of the polygon.

Cut it into smaller shapes, such as triangles or other quadrilaterals using angles. Find the area of each smaller shape, then add the areas together to find the area of the whole shape.

Assuming it's not a square or rectangle, you would have to subdivide the figure into smaller sections consisting of squares, rectangles, triangles, and other shapes whose areas can be easily calculated. Then add those areas together.

Polygons with more than three sides cannot be determined from side lengths alone. You need to know some of the angles.

a=1/2ap. a=apothem (like the radius except it comes from the middle of a side). p=perimeter.

Not sure which formula you mean. Here's a trig formula that will work for any regular polygon if you know the length of a side: A = s²n / [4 tangent(180°/n)], where s is the length of a side, and n is the number of sides. Here's a trig formula that will work if you know the radius of the polygon (distance from the center to any vertex): A = r²n [sine(360°/n)] / 2, where r is the radius, and n is the number of sides. Finally, here's a trig formula that will work if you know the apothem of the polygon (perpendicular distance from the center to any side): A= a²n[tangent(180°/n)], where a is the length of the apothem, and n is the number of sides.

Part 3 above has nothing to do with circles. Any circle with a 7 cm radius has an area of 49π or 153.937 square centimeters.

There are two ways: Mentally cut the polygon up into other shapes that are easy to calculate, such as triangles and squares. Then calculate each part and sum up the results. Another approach you might take is to imagine the polygon is a shape that can be easily calculated, such as a square. Then find the area of the square. Next, subtract the area you used to fill the square from the square.

Write down the formula for finding the area of a regular polygon. To find the area of a regular polygon, all you have to do is follow this simple formula: area = 1/2 x perimeter x apothem. Here is what it means: Perimeter = the sum of the lengths of all the sides.

The formula for the area of a regular octagon is 4.828 s², where s is the length of any side. (If the octagon is not regular, no area formula is available.)

If sides intersect with each other, it is not a polygon. Polygons can only intersect at vertices, not in the sides. Otherwise, it is not a polygon, so the formula won't work.

The area of a parallelogram is base times height. It is basically just an oblique rectangle, so the area is the same as any rectangle with the same base and height.

Area, by definition, must be non-negative. If you use the 'shoelaces' formula from Part 3, you will get a negative answer if you connect the vertices in the reverse order. The absolute value of that answer is the true area of that shape. Most other area formulas make it mathematically impossible to return a negative answer, except perhaps if you plug in a negative number for a length which violates the same general principle as a negative area.

Finding the area of a triangle requires the height as well as the base.

If that formula means "length times width," that would apply to a rectangle (and square).