Area of Regular Polygons

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Area of Regular Polygons. Break the figure down into triangles. 4. 5. 3. 6. 2. 1. Notice there are 6 triangles and 6 sides. 4. 5. 3. 6. 2. 1. Let’s look at 1 of the triangles closer. The area of a triangle is:. h. b. Area = ½bh.
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Area of Regular PolygonsBreak the figure down into triangles453621Notice there are 6 triangles and 6 sides453621Let’s look at 1 of the triangles closerThe area of a triangle is:hbArea = ½bhWhen the triangle is part of a polygon, the height is called the ApothemapothemhbThere are 6 triangles, so we have to multiply our area by 6!apothembaseOf course, using the equation you’ll only find the area for one of the triangles. Another way to look at it is that we have 6 bases and one apothemapothembaseRemember, 6 times the base is the perimeter of the object!Therefore we can use the formula:apothembase1__apArea =2PerimeterEx: Find the area of the hexagon851__apArea =2First we must find the perimeter:p = 5(6) = 30Find the area of the hexagon8511____ap8(30)Area =Area =22Plug everything inp = 5(6) = 30Find the area of the hexagon851__8(30)Area =2Solve= 120Practice 1
  • Find the area of the following regular polygons:
  • Octagon with base of 4 and apothem 7
  • Hexagon with base of 8 and apothem 3
  • The figure below
  • 1210But what if we’re not given the apothem??1__apArea =2Ex: Find the area of the polygon101__apArea =We need the perimeter and apothem2453621Let’s look at 1 of the triangles closer againa10Inside we have two right trianglesWe can find the angle at the top and use it to find the apothema10There’s 3600 around the center of the figureSince there’s 6 sides we can find the angle at the top of each triangle by:360= 606600The top angle is 60 and the apothem cuts it in halfa300300Half the triangle means half the basea5This is now a 30-60-90 right triangle!The apothem is:Ex: Find the area of the polygon101__apArea =2We need the perimeter and apothemEx: Find the area of the polygon101__apArea =26But what if it’s not a special right triangle??1__apArea =2360= 725360Break it down to the small trianglea3The angle gets cut in halfThe base is cut in half360Use the trig function to find apothemhypaadj3opp
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