An apothem is a distance from the center of the polygon to the mid-point of a side. The apothem its the distance between the center of the geometric figure and the closest point in the figure to the center. Also, the area can be calculated in The word 'apothem' can also refer to the length of that line segment. area = n * a * ri / 2, having ri - incircle radius (it's also an apothem - a line segment from the center to the midpoint of one of its sides) area = perimeter * ri / 2 , given ri and polygon perimeter : ) Step-by-step explanation: a=apothem s = 2 sqrt3 a# #"Area of equilateral triangle " A_t = (sqrt3 s^2 ) / 4# Substituting for s in terms of a, #A_t = (sqrt3 / 4) * (2 sqrt3 a)^2# #A_t = (sqrt3 * cancel4 * 3 * a^2) / Geometry. Area of a polygon calculator finds the perimeter and area of a regular polygon. Octagon Area = 2 * (1 + 2) * a; The octagon area may also be calculated from: Octagon Area = perimeter * apothem / 2. a = S / (2*tan(180/n)) Where a is the apothem; S is the length of any side if you do not have the perimeter then you can find it by multiplying # of sides and length of sides. A perimeter in octagon case is simply 8 * a. #:. side length = apothem * sqrt(3)/2 = 12 And what is an apothem? Geometry. A Polygon is a closed plane figure having three or more sides. Area Definition. Find the surface area of a right octagonal pyramid with height 2.5 yards, and its base has apothem length 1.5 yards. You said you only know the apothem; you actually know the apothem (the height of the triangles) and the angles in the triangles. Turn the regular polygon into congruent iscoceles triangles. It is the space of the internal surface in a figure, it is limited for the perimeter. Using apothem and length of a side : Area of Polygon = (A * P) / 2 where A = side / (2 * Tan ( / N)) where, N = Number of sides, A = Apothem, R = Radius, P = Perimeter. Area=1/2 * Perimeter* Apothem Perimeter=base of octagon* number . With a bit of trig you can find the area of each triangle. The following formula can be used to calculate an apothem of any polygon. Round the answer to the nearest inch. Properties of apothems. Apothem Formula. Polygon & Apothem Definition: Polygon is a closed plane figure having three or more sides. There are multiple ways to found the Apothem of a Regular Polygon. What is the area of a regular pentagon with an apothem 14 inches long and a side 20 inches long? An Apothem is a line segment from center point of side of a regular polygon to the midpoint of the regular polygon. Answer: To Find the area you would need to use Area= 1/2 a multiplied by the perimeter. Hope this helps. Question 1027055: Find the area of a hexagon with an apothem of (8)(sqrt3) Found 2 solutions by CubeyThePenguin, ikleyn: Answer by CubeyThePenguin(3113) (Show Source): You can put this solution on YOUR website! #"Apothem " a = s / (2 * sqrt3)# where s is the length of the side of an equilateral triangle. If you know the length of the perimeter in a decagon and the area, you can calculate its apothem using the following formula: $$"apothem" = (2a)/p $$ Perimeter and Area Length Apothem result Calculate Reset Copia y pega el siguiente cdigo en el HTML de tu pgina web para mostrar ah esta frmula y The apothem a can be used to find the area of any regular n-sided polygon of side length s according to the following formula, which also states that the area is equal to the apothem multiplied by half the perimeter since ns = p. = =. Apothem Definition.