Finding the area of regular polygons. Finding area of regular polygons. Review of Prior Knowledge Regular Polygon : a polygon in which all sides and angles are congruent. New Vocabulary Radius – a line connecting the center of a polygon with a vertex.
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Step 1: Break the polygon into triangles. Draw in the radii and one apothem.
Step 2: Remove one triangle from the polygon.
Step 3: Find lots of angles!! Transfer them onto the triangle.
Step 4: Find the sides of the triangle using special rules.
Step 5: Find the area of the yellow triangle…
Step 6: So, the total area = 6 ( ) = sq units
There are 6 triangles in a hexagon so in order to find each angle in the center divide 360 by 6. Each is 60.
The 60 on top of the triangle needs to be split in two equal parts.
Area = ½ (10)( ) =
There are 6 of these triangles.
1. Break the polygon into triangles by drawing in the radii.
2. Remove one triangle from the polygon
3. Fill in lots of angles.
4. Find the area of the removed triangle by finding the base and height of the triangle.
5. Find the area of the entire polygon by multiple the area of one triangle by the number of triangles.
Area of triangle = ½ ( )(4) =
Area of polygon = (# of triangles)(area of yellow triangle)
= 3 ( ) = square units
360 / 3 = 120
Use the 30-60-90 rules
Area = 128 square units
Area = square units
Area = square units
Area =(# of tri’s)(area of one tri)
(# of tri’s) = (# of sides) so…
Area =(# of sides)(area of one tri)
(area of one tri) = ½ bh so…
Area =(# of sides)( ½ bh)
we can multiply in any order so…
Area = ½ (h) (# of sides)(b)
the height (h) is the same as the apothem so…
Area = ½ (a) (# of sides)(b)
(# of sides)(base) = the perimeter so…
Area = ½ (a) (p)