AREA OF REGULAR POLYGON WORKSHEET

Find the area of each of regular polygon.

Problem 1 :

Solution

Problem 2 :

Solution

Problem 3 :

Solution

Problem 4 :

The game at the right has a hexagon shaped board. Find the area.

Solution

Problem 5 :

Each of the tiles in the game is also a regular hexagon. Find the area of one of the tiles if the sides are each 0.9 inches long and each apothem is 0.8 inches long.

Solution

Problem 6 :

Find the area of the shaped region in the regular polygon at below.

Solution

Problem 7 :

Find the area of the shaped region in the regular polygon at the below.

Solution

Problem 8 :

Find the area of the shaped region in the regular polygon at the below.

Solution

Problem 1 :

What is the area of regular nanagon with 10 cm sides.

Solution

Problem 2 :

Octagon with side length 6 cm

Solution

Problem 3 :

Decagon with side length 4 yd

Solution

Problem 4 :

The Pentagon in Arlington, Virginia, is one of the world’s largest office buildings. It is a regular pentagon, and the length of each of its sides is 921 ft. what is the area of land that the Pentagon covers to the nearest thousand square feet?

Solution

Problem 5 :

find the area of the shaded region.

Problem 6 :

Problem 7 :

Problem 1 :

Name of the shape = pentagon, length of apothem = 7.3 cm and side length = 10.6 cm

Solution

Problem 2 :

Name of the shape = triangle, length of apothem = 14 cm and side length = 28√3 cm

Solution

Problem 3 :

Name of the shape = 7-gon, length of apothem = 21.8 cm and side length = 21 cm

Solution

Problem 4 :

Name of the shape = octagon, length of apothem = 14.1 cm and side length = 11.7 cm

Solution

Problem 5 :

You are decorating the top of a table by covering it with small ceramic tiles. The tabletop is a regular octagon with 15-inch sides and a radius of about 19.6 inches. What is the area you are covering?

Solution

Problem 6 :

A regular nonagon is inscribed in a circle with a radius of 4 units. Find the area of the nonagon.

Solution

Find the area of the shaded region.

Problem 7 :

Solution

Find the area of the shaded region.

Problem 8 :

Solution

Example 9 :

Describe and correct the error in finding the area of the regular hexagon.

Solution

Find the area of each polygon with given radius. Leave the answer in radical.

Problem 1 :

Solution

Problem 2 :

Solution

Problem 3 :

Solution

Problem 4 :

A regular nonagon has a perimeter 45 inches and its apothems are each 6  9/10 inch long.

a) Find the area 

b) Round the length of an apothem to the nearest inch and find the area. How does it compare to the original area ?

Solution

Problem 5 :

The area of a regular octagon is 392.4 square meters, and an apothem is 10.9 meters long

a) Find the perimeter 

b) Find the length of one side

Solution

Problem 6 :

Find the approximate area of Fort Jefferson in Dry Tortugas National Park, Florida, if each side is 460 feet long and an apothem is about 398 feet long.

Solution

Problem 7 :

The petals in the flower form a polygon that is approximately a regular pentagon with an apothem 3.4 cm long.

a) Find the approximate area of the pentagon.

b) There are five triangles in the pentagon that are not part of the flower. Assume that they have equal areas and have a height of 1.5 cm. Find the total area of triangles.

c) What is the approximate area of the flower.

Solution