Finding Areas of Regular Polygons, and Circles as Part of Composite Figures.

What would you do if your dad, or mom told you to calculate how many square feet of paint will be needed to paint the front of your house? What if some of the windows were circular, some rectangular, and some like a pentagon, or hexagon? Would you be able to apply the formula for the area of regular polygons? Do you know what is the apothem? Do you remember how to find perimeters?

In the beginning this lesson teaches how you may find areas of regular polygons, and circles. At the end you will view examples involving the front of a house, and of composite figures (Several figures in one complex figure).

Lesson's Content

Lesson's Glossary

Angle
Geometric shape formed by two rays (initial and ending sides of the angle) that share a common endpoint called the vertex. You may name an angle using the vertex, or a point in each ray and the vertex label in the center.

Area
The amount of space taken up in a plane by a figure.

Circle
The set of points on a plane at a certain distance (radius) from a certain point (center); a polygon with infinite sides

Circumscribed circle or circumcircle of a polygon: A polygon is circumscribed about a circle if all the sides are tangent to the circle, and a circle is circumscribed about a polygon if all the vertices of this are on the circumference of the circle.

Concave polygon
If a polygon has diagonals that lie outside the polygon then the polygon is concave.

Convex polygon
A convex polygon is any polygon that is not concave.

Decagon
A ten-sided polygon.

Dodecagon
A twelve-sided polygon.

Heptagon
A seven-sided polygon.

Hexagon
A six-sided polygon.

Inscribed planar shape or solid: A polygon is inscribed in a circle if the vertices of a polygon inside a circle are on the circumference of the circle; a circle is inscribed to a polygon if all the sides of the polygon are tangent to the circle in the interior of the polygon.

irregular polygon
An irregular polygon is any polygon that is not regular.

N-gon
A polygon with n sides.

Nonagon
A nine-sided polygon.

Octagon
An eight-sided polygon.

Pentadecagon
A 15-sided polygon.

Pentagon
A five-sided polygon.

Polygon
A polygon is a two-dimensional geometric figure with these characteristics:
It is made of straight line segments.
Each segment touches exactly two other segments, one at each of its endpoints. 
It is closed -- it divides the plane into two distinct regions, one inside and the other outside the polygon.

Radii
Plural form of radius.

Radius
The segment whose endpoints are any point on a circle or sphere and its center; the length of that segment

Regular polygon
A regular polygon has sides that are all the same length and angles that are all the same size.

Quadrilateral
A four-sided polygon.

Septagon
A seven-sided polygon.

Side of a polygon
A single segment from the union that forms a polygon.

Vertex of a polygon
An endpoint of a segment in a polygon.

Interactive Geometric Applets: Relevant Theorems.

A regular pentagon has 5 congruent sides, and 5 congruent angles. In this interactive applet

you will view in a dynamic way relationships among sides, angles, and angle-side.

A regular hexagon has 6 congruent sides, and 6 congruent angles. Drag the slider

in this interactive geometric applet to find out how the relationships in the

hexagon work. You will know about the role of the radius, the apothem, and perimeter

in finding the area of the hexagon.

A regular octagon has eight sides congruent, and eight angles congruent. You may play

with this interactive geometric applet to verify the relationships that exist among

the different elements in the figure.

Vocabulary Puzzle Interactive

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