Q&A for How to Find the Area of Regular Polygons

Since a regular polygon has congruent sides (every side is equal to each other) you set up the equation 5-2x = -4x+9 then you solve for "x". After solving for "x", you substitute the answer you got from "x" back into the one of the expressions from one of the sides. You should get the answer of how many units one of the sides is. After that, just multiply that answer by how many sides the polygon has to get your perimeter.

The perimeter equals the side length times the number of sides. In this case, multiply 21 by 9 and you will get a perimeter of 189.

Since the given measurements of the sides best represents a trapezoid, you use the area of a trapezoid equation A=h*((b1+b2)*0.5) where A is the area, h is the height of the trapezoid, and where b1 is the top base and b2 is the bottom base. To find the height, you subtract b2 by b1, then divide it, then substitute that answer into "a" of the Pythagorean theorem a^2+b^2=c^2, where "c" equals the length of the side of your trapezoid which in this case is 3m. You solve for b in that equation to get your height. Once you got the measurement of the height of the trapezoid, you use the area of a trapezoid equation and substitute your answers in it to get your area.

Find the radius of circle using volume of circle formula (pi*(r)^2), which is equal to 158.9 (here, r = 7.09). Radius of circle = length of one of the side of regular hexagon. Then, using the area formula (area=(a*p)/2), calculate its area (here, 130.59).

The only equation is the general equation for any regular polygon as given in Part 1 above.

To get the area, multiply the perimeter of the nonagon by the apothem and then divide by 2. You get the perimeter by multiplying 4 by 9, getting 36. The apothem is 4/(2Tan(180/9)), which equals 5.5. Now you get area = (5.5 x 36)/2, which is 99.

To find the answer to this question, I used the formula A=(b^(2)ncos^(2)(180/n))/2sin(360/n) in the which perimeter is bn, so b=p/n. I filled out the formula with the same P in both the triangle's formula and the hexagon's and put in the constant j as the multiple of the two so the area of the hexagon = j x the area of triangle. Eventually I came out with j=1.5, so the hexagon would be 1.5 times the size of the triangle.

If you have no actual numbers to work with, you can't find the area.

Here the diameter (12 units) of the circumscribing circle is the diagonal of the square. Since the diagonal is sqrt(2) = 1.414 times the side of the square, the area of the square is 0.5 * 12 * 12 = 72 sq. units.

If you know the perimeter, multiply it by the apothem, then divide by two. That equals the area of the polygon.

You also need the perimeter. See Method 2 in the wikiHow article on how to Calculate the Area of a Hexagon .

You would need more information than that.

The general equation for the area of any regular polygon given above does not involve trigonometry.

Area of an regular polygon is number of sides * length of a side. Number of sides = 8, and one side = 4 cm, therefore area is 8 * 4 = 32 cm.

The radius = 1 side of the pentagon. Use the procedures of finding the value of apothem described above.

If you mean apothem, rather than radius, refer to method 1. Radius implies a circle. To find the area of a circle, square the radius and multiply by π.

Apply the formula that shows how to find the Apothem of Part 2; just ignore the area of the polygon.

You would need to find one of the angles and use trigonometry to find the length of half the side length, since the apothem bisects the side. Then, you'd use the side length multiplied by the number of sides to get the perimeter, and since A=ap/2, where A is area, a is apothem, and p is the perimeter, you'd plug those in to find the area.

(25 cm)(4) = 100 cm.