10.3 & 10.4 Area of Regular Polygons & Perimeter/Area of Similar Polygons
The radius of a regular polygon is a segment that connects the polygon’s center to one of its vertices. The apothem of a regular polygon is a segment that connects the center of the polygon to one of the sides and is perpendicular to it.
**The number of radii and apothems that a regular polygon has is dependent upon the number of sides!
Important Property of the Radius:
· It bisects the interior angle that it connects to.
Important Properties of the Apothem:
· It bisects the side of the polygon that it connects to.
· It bisects the angle formed by two radii.
Examples: Use the properties of the radius and apothem to find the missing angles.
1. 2. 3.
The Area of any regular polygon =
· p is the perimeter of the regular polygon
· a is the apothem length
Examples: Find the area of each regular polygon:
1. hexagon, a = 2.6 ft, s = 3 ft 2. nonagon, a = 5.6 mm, s = 4.1 mm
3 4. 5.
6. 7.
For a pair of similar figures:
If the scale factor between the two figures is:, then:
The ratio of the perimeters of the figures is:
The ratio of the areas of the figures is:
Example: Find the scale factor from the polygon on the left to the polygon on the right. Then find the scale factor for the perimeters and areas of each.
1. 2.
Examples: Find the area of the other similar polygon, given the area of one polygon.
1. the Area of larger triangle = 75 cm2
2. Area of smaller octagon = 288 ft2
Examples: Given the areas of two similar polygons, find the scale factor and the ratio of the perimeters of the polygons.
1. two regular pentagons with areas 50 in.2 and 162 in.2
2. two equilateral triangles with areas 8 cm2 and 128 cm2
Assignment: text pg.632 #8-10, 11-27 odd, 31, 34, 37, 39, 44, 45, 49, and pg.638 #9-29 odd, 36, 52-55
Warm-Up 04/27/2012
1. Classify the following quadrilateral and find its area:
2. Find the value of h:
3. Find the area for the figure below. Round your answer to one decimal place:
4. Find the area of the rhombus below in simplest radical form:
5. One base of a trapezoid is 5 less than twice the other base. The height is 3 cm. The area is 75 cm2. Find the length of each base. They will be decimals!
Pre-Requisites!!!
1. Find the missing sides of each special right triangle in radical form:
2. What is a regular polygon? Two Characteristics!!
3. What is the sum of the angle measures of a quadrilateral, a pentagon, and a hexagon?
4. How could you find the angle measures of one interior angle of a regular polygon if you know the sum of the angle measures?