First you must determin what the "apothem" is, and by that i mean what the hell that word means.
Area in square units = 0.5*(apothem)*(perimeter)
You can find the area of any regular polygon with this equation: 1/2ap where a is the apothem and p is the perimeter.To find the perimeter, multiply 7 times 12 to get 84.To find the apothem, divide 360 (the amount of degrees around the center of the polygon) by 7 (the amount of sides you have) to get about 51.43. This gives you the measure of the angle of one triangle connected to 2 adjacent vertices. You have to make this a right triangle so that you can use trigonometry to find the apothem, so divide that angle by 2 to get 25.72. You know the side opposite of this angle is 6 because it is half the amount of the side (remember we divided this triangle by 2). To find the apothem at this point, use trigonometry. tan25.72 = 6/x. The apothem is 12.46.So, plug all of this into your calculator; a = 1/2(84)(12.46). You find the area to be about 523.3.
7
If you mean an apothem of 4.82 inches rounded to two decimal places then its area is 0.5*4.82*7*5 = 84.35 square inches.
Area of regular 8 sided octagon: 0.5*7*5.8*8 = 162.4 square units Not that in fact by using trigonometry the apothem is slightly bigger than 7
In general you would need to select a vertex of the nonagon and join it to the other vertices (except the two adjacent ones). This will divide the nonangon into 7 triangles. Measure the sides and/or angles of these triangles and calculate their areas. Add these together to get the area of the nonagon.If the nonagon is regular then there are formulae to calculate its area. These depend on whether you know the side length, apothem or circumradius.
Area in square units = 0.5*(apothem)*(perimeter)
You can find the area of any regular polygon with this equation: 1/2ap where a is the apothem and p is the perimeter.To find the perimeter, multiply 7 times 12 to get 84.To find the apothem, divide 360 (the amount of degrees around the center of the polygon) by 7 (the amount of sides you have) to get about 51.43. This gives you the measure of the angle of one triangle connected to 2 adjacent vertices. You have to make this a right triangle so that you can use trigonometry to find the apothem, so divide that angle by 2 to get 25.72. You know the side opposite of this angle is 6 because it is half the amount of the side (remember we divided this triangle by 2). To find the apothem at this point, use trigonometry. tan25.72 = 6/x. The apothem is 12.46.So, plug all of this into your calculator; a = 1/2(84)(12.46). You find the area to be about 523.3.
7
An octagon with a side length of 5.8 cm has an apothem that is approximately 7 cm. The area of such a shape is approx 162.4 sq cm.
If you mean an apothem of 4.82 inches rounded to two decimal places then its area is 0.5*4.82*7*5 = 84.35 square inches.
Area of regular 8 sided octagon: 0.5*7*5.8*8 = 162.4 square units Not that in fact by using trigonometry the apothem is slightly bigger than 7
An octagon with a side length of 5.8 cm has an apothem that is approximately 7 cm. The area of such a shape is approx 162.4 sq cm.
The area is 162.4 square inches.If apothem = x, then area = 8*x^2*tan(180/8)If side = s, then area = 8*s^2/(4*tan(180/8))
By Apothem LengthThe area of a regular octagon can also be computed using its measured apothem (a line from the center to the middle of any side). The formula for an octagon with side length s and apothem a is Area = a4s (apothem times one-half the perimeter)So for this example, (7 cm and 8.45 cm) Area = (8.45)(28) = 236.6 cm2----By Side LengthThe area of a regular octagon with side length s is given as Area = 4.828427 s2 , so for a regular octagon of side length 7 cm , the area is also about 236.6 cm2.(This formula is generated by adding or subtracting the missing corner triangles.)
The area of a regular octagon: A = (2 x apothem)2- (length of side)2 or in this case A= (2 x 8.45)2 - 72
293.72