1. Warm-Up#31
1. To estimate the height of a tree, Dave stands in the shadow of the tree so that his shadow and the tree’s shadow end at the end point. Dave is 5 feet 2 inches tall and his shadow is 12 feet long. If he is standing 40 feet away from the tree, what is the height of the tree? 2. In the triangle below, line segment MN is parallel to line segment BC. Solve for x.

2. Find the area of Regular Polygons

3. Areas of Regular Polygons
What You'll Learn
You will learn to find the areas of regular polygons.
Vocabulary
1) center
2) apothem

4. Areas of Regular Polygons
center
Every regular polygon has a ______,
a point in the interior that is equidistant
from all the vertices.
A segment drawn from the center that is perpendicular to a side of the regular
polygon is called an ________.
apothem
congruent
In any regular polygon, all apothems are _________.

5. Areas of Regular Polygons
Theorem 10-5
Area of a
Regular Polygon
If a regular polygon has an area of A square units, an apothem of a units, and a perimeter of P units, then P

6. Areas of Regular Polygons
Now, create a triangle by drawing segments from the center to each vertex on
either side of the apothem.
Now multiply this times the number of triangles that make up the regular polygon.
The area of a triangle is calculated with the following formula:
The figure below shows a center and all vertices of a regular pentagon.
An apothem is drawn from the center, and is _____________ to a side.
perpendicular
There are 5 vertices and each is 72° from the other (360 ÷ 5 = ___.) 72
72°
72°
72°
72° s a
72°
What measure does 5s represent?
perimeter
Rewrite the formula for the area of a pentagon using P for perimeter.

7. Areas of Regular Polygons
Find the area of the shaded region in the regular polygon.
5.5 ft
8 ft
Area of polygon
Area of triangle
triangle
To find the area of the shaded region, subtract the area of the _______
from the area of the ________:
pentagon
The area of the shaded region:
110 ft2 – 22 ft2 =
88 ft2

8. Areas of Regular Polygons
Find the area of the shaded region in the regular polygon.
Area of polygon
Area of triangle
6.9 m
8 m
triangle
To find the area of the shaded region, subtract the area of the _______
from the area of the ________:
hexagon
The area of the shaded region:
165.6 m2 – 55.2 m2 =
110.4 m2