You will be able to

•Calculate areas of regular polygons.

• Calculate areas of composite figures.

• center of a regular polygon

• radius of a regular polygon

• apothem

• central angle of a regular polygon

Identify Segments and Angles in Regular Polygons

In the figure, pentagon PQRST is inscribed in Identify the center, a radius, an apothem, and a central angle of the polygon. Then find the measure of a central angle.

A. mDGH = 45°

B. mDGC = 60°

C. mCGD = 72°

D. mGHD = 90°

In the figure, hexagon ABCDEF is inscribed in Find the measure of a central angle.

Area of a Regular Polygon

FURNITURE The top of the table shown is a regular hexagon with a side length of 3 feet and an apothem of 1.7 feet. What is the area of the tabletop to the nearest tenth?

A. 6 ft2

B. 7 ft2

C. 8 ft2

D. 9 ft2

UMBRELLA The top of an umbrella shown is a regular hexagon with a side length of 2 feet and an apothem of 1.5 feet. What is the area of the entire umbrella to the nearest tenth?

Use the Formula for the Area of a Regular Polygon

A. Find the area of the regular hexagon. Round to the nearest tenth.

A. 73.1 m2

B. 96.5 m2

C. 126.8 m2

D. 146.1 m2

A. Find the area of the regular hexagon. Round to the nearest tenth.

• composite figure

Find the Area of a Composite Figure by Adding

POOL The dimensions of an irregularly shaped pool are shown. What is the area of the surface of the pool?

A. 478.5 ft2

B. 311.2 ft2

C. 351.2 ft2

D. 438.5 ft2

Find the area of the figure in square feet. Round to the nearest tenth if necessary.

Find the Area of a Composite Figure by Subtracting

Find the area of the shaded figure.

A. 168 ft2

B. 156 ft2

C. 204 ft2

D. 180 ft2

INTERIOR DESIGN Cara wants to wallpaper one wall of her family room. She has a fireplace in the center of the wall. Find the area of the wall around the fireplace.