G - 10.4 Area of Regular Polygons

Areas of Regular Polygons
Section 10.4

Regular Polygons

You can circumscribe a circle about any regular polygon.
The center of a regular polygon is the center of the circumscribed circle.
The radius is the distance from the center to a vertex
The apothem is the perpendicular distance from the center to a side.

Multiple Choice

The black arrow points to the

• center

• radius

• apothem

Multiple Choice

The blue arrow points to the

• center

• radius

• apothem

Multiple Choice

The red arrow points to the

• center

• radius

• apothem

Finding Angle Measures

The figure at the right is a regular pentagon with radii and an apothem drawn. Find the measure of each numbered angle.

Multiple Choice

In the diagram, a portion of a regular octagon has radii and an apothem drawn. Find the measure of angle 1.

• 45

• 22

• 22.5

• 67.5

Multiple Choice

In the diagram, a portion of a regular octagon has radii and an apothem drawn. Find the measure of angle 2.

• 45

• 22

• 22.5

• 67.5

Multiple Choice

In the diagram, a portion of a regular octagon has radii and an apothem drawn. Find the measure of angle 3.

• 45

• 67.5

• 22.5

• 68

Multiple Choice

In the diagram, a portion of a regular octagon has radii and an apothem drawn. Find the measure of angle 3.1

• 120

• 60

• 30

• 15

Multiple Choice

In the diagram, a portion of a regular octagon has radii and an apothem drawn. Find the measure of angle 2.

• 45

• 67.5

• 22.5

• 68

Multiple Choice

In the diagram, a portion of a regular octagon has radii and an apothem drawn. Find the measure of angle 3.1

• 120

• 60

• 30

• 15

Regular Polygons

Regular Polygons

Multiple Choice

The perimeter of a regular polygon is

• P = 2b + 2h

• $$P=\frac{1}{2}h\left(b_1+b_2\right)$$

• $$P=\frac{1}{2}ap$$

• $$P=ns$$

Multiple Choice

The area of a regular polygon is

• A = bh

• $$A=\frac{1}{2}h\left(b_1+b_2\right)$$

• $$A=\frac{1}{2}ap$$

• $$A=ns$$

Finding the area of Regular Polygons

Find the area of a regular decagon with a 12.3 in apothem and 8 in sides.

Multiple Choice

Find the area of a regular pentagon with 11.6cm sides and 8cm apothem

• 92.8cm²

• 232cm²

• 384cm²

• 200cm²

Application

Some boats used for racing have bodies made of a hineycomb of regular hexagonal prisms sandwiched between two layers of outer material. In the diagram, there is the end of one hexagonal cell. Find its area.

Application

The smaller triangles in the Minneapolis sculpture at the left are equilateral. Each has a 12.7 in radius. What is the area of each to the nearest square inch.

Exit Ticket

Find the area of a regular pentagon with 7.2-ft sides and a 6.1 ft radius.