Formula of apothem
WebThe apothem is the perpendicular line that connects the center of the hexagon with one side. The apothem can be very useful when we want to find the area of a hexagon since it allows us to use a simpler formula. … WebApr 26, 2009 · 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 …
Formula of apothem
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WebOct 14, 2024 · To calculate the apothem of a hexagon, start by dividing the hexagon into 6 triangles. Then, divide one of the triangles in half to … WebDec 13, 2024 · If all that is known is the number of sides and the side length, there is a formula for this as well. a = s 2tan(180 n) a = s 2 t a n ( 180 n) Where a = apothem, s = length of one side, and n =...
WebFeb 11, 2024 · The formula for the area of a polygon is always the same no matter how many sides it has as long as it is a regular polygon: area = apothem × perimeter / 2; Just as a reminder, the apothem is the … WebSep 4, 2024 · The area of a regular polygon is one-half the product of the apothem and the perimeter. A = 1 2aP Proof Example 7.1.3 Find the area of a regular pentagon with side 20, to the nearest tenth. Solution From Example 7.1.2 we know a = 13.764. The perimeter P = (5)(20) = 100. Therefore A = 1 2aP = 1 2(13.764)(100) = 1 2(1376.4) = 688.2. Answer: …
WebGiven the apothem (inradius) If you know the apothem, or inradius, (the perpendicular distance from center to a side. See figure above), the area is given by: area = a 2 n tan 180 n where a is the length of the apothem (inradius) n is the number of sides tan is the tangent function calculated in degrees (see Trigonometry Overview ). WebJul 15, 2024 · Explanation: Apothem a = s 2 ⋅ √3. where s is the length of the side of an equilateral triangle. ∴ s = 2√3a. Area of equilateral triangle At = √3s2 4.
WebIf you know the length of one of the sides, the area is given by the formula: where s is the length of any side n is the number of sides tan is the tangent function calculated in …
WebThe formula to calculate the area of a regular hexagon with side length s: (3 √3 s^2)/2 Remember, this only works for REGULAR hexagons. For irregular hexagons, you can break the parts up and find the sum of the areas, depending on the shape. Hope that helped! 3 comments ( 26 votes) Upvote Downvote Flag more Show more... freyawolf 10 years ago reflector\u0027s jwreflector\u0027s irWebOct 10, 2024 · If we know the length of the apothem and perimeter of a regular polygon, we can calculate the area of the polygon using the formula: A = (1/2) aP where a is the length of the apothem and P is... reflector\u0027s ixWebTo find the formula for the apothem, we can use the diagram of a pentagon: Here, we divide the pentagon into five congruent triangles and use one of the triangles to find the apothem. We can see that the … reflector\u0027s k0WebAns-To find the area of a hexagon with apothem 4, we can use the formula: A r e a = ( 1 2 ) × a p o t h e m × p e r i m e t e r The perimeter of a regular hexagon can be found by multiplying the length of one side by 6. reflector\u0027s k1WebArea of Pentagon using Apothem. If the side-length and apothem is given of a pentagon, then; Area of Pentagon = 5/2 x s x a; where ‘s’ is the side of the pentagon, and ‘a’ is the apothem length. Apothem is the line from the center of the pentagon to a side, intersecting the side at 90 degrees right angle. reflector\u0027s k3WebThe area of any regular polygon can be calculated using the length of its apothem and the length of one of its sides. The area formula in these cases is: A=\frac {1} {2}nal A = 21nal. where a is the length of the apothem, l is the length of one of the sides and n is the number of sides of the polygon. This formula is derived from the fact that ... reflector\u0027s k4