11.2a area of regular polygons ccsslesson goals understand that to find the area of a regular...
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11.2a Area of Regular Polygons
CCSS LESSON GOALS Understand that to find the
area of a regular polygon you find the area of one triangle and multiply that area by the number of sides the polygon has.
ESLRs: Becoming Effective Communicators, Competent Learners and Complex Thinkers
G GPE 7: Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.
definition
Center of a Polygon is the center of its circumscribed circle.
Radius of a Polygon is the radius of its circumscribed circle.
definition
The Apothem of a Polygon is the distance from the center to any side of the polygon.
radius
apothem
definition
Central Angle of a Regular Polygonis an angle whose vertex is the center and whose sidescontain two consecutive vertices of the polygon.
definition
The Measure of a Central Angle of a Regular Polygon
72o 360
n
360
5
ExampleFind the area of the triangle.
12A bh
12 2 3
3 square units1
3
Example
12A bh
12 6 3 3
9 3 square units
3 3
3
Find the area of the triangle.
Area of a Regular Polygon1. Divide the polygon into congruent triangles by drawing
the radii of the polygon
2. Find the measure of the central angle.
3. Draw the apothem.What happens to the central angle?
4. Find the length of the apothem
5. Find the area of one inner triangle.
6. Multiply by the number of sides.
Area of a Regular PolygonFind the area of a regular hexagon with side length of 4 yds.
1. Divide the polygon into congruent triangles by drawing the radii of the polygon.
4 yds
360
6
Area of a Regular Polygon
2. Find the measure of the central angle.
360
n
60
4 yds
Find the area of a regular hexagon with side length of 4 yds.
Area of a Regular Polygon
3. Draw the apothem.
60
What happens to the central angle?
12 6030
4 yds
Find the area of a regular hexagon with side length of 4 yds.
Area of a Regular Polygon
What happens to the base?
12 42 yds
30
4 yds
3. Draw the apothem.
Find the area of a regular hexagon with side length of 4 yds.
Area of a Regular Polygon
4. Find the length of the apothem.
30
22 3
4 yds
Find the area of a regular hexagon with side length of 4 yds.
4 yds
Area of a Regular Polygon5. Find the area of one inner triangle.
12 4 2 3A
2 3
4 3
4 yds
Find the area of a regular hexagon with side length of 4 yds.
Area of a Regular Polygon6. Multiply by the number of sides/triangles.
6 4 3A
4 yds
224 3 yd
4 3
4 yds
Find the area of a regular hexagon with side length of 4 yds.
Area of a Regular PolygonFind the area of a square with a radius 6 units.
1. Divide the polygon into congruent triangles by drawing the radii of the polygon.
Area of a Regular Polygon
2. Find the measure of the central angle.
Find the area of a square with a radius 6 units.
Area of a Regular Polygon
3. Draw the apothem.What happens to the central angle?
Find the area of a square with a radius 6 units
Area of a Regular Polygon
4. Find the length of the apothem.
Find the area of a square with a radius 6 units
2
2
Area of a Regular Polygon5. Find the area of one inner triangle.
Find the area of a square with a radius 6 units
18A
Area of a Regular Polygon6. Multiply by the number of sides/triangles.
4 18A
272 units
Find the area of a square with a radius 6 units.
Area of a Regular PolygonThe area of a regular polygon can be found using
n = the number of sidess = the length of a sidea = the length of the apothem
a = the length of the apothem P= perimeter of the polygon
Today’s Assignment #3
p.672: 1 – 5, 9, 10, 16, 18, 22, 30