AREA OF REGULAR POLYGON WITH GIVEN SIDES WORKSHEET

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.

Solution

Problem 6 :

Solution

Problem 7 :

Solution

Find the perimeter area of each regular polygon. Leave your answer in simplest form.

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

Problem 8 :

Solution

Problem 9 :

Problem 10 :

Octagon with side length 6 cm

Solution

Solution

Problem 2 :

Solution

Problem 3 :

Solution

Problem 4 :

Solution

Problem 5 :

Solution

Problem 6 :

Solution

Problem 7 :

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 8 :

Use the diagram.

a) Identify the center of polygon JKLMN.

b) Identify a central angle of polygon JKLMN.

c) What is the radius of polygon JKLMN?

Solution

Problem 9 :

Find the area of the shaded region.

Solution

Problem 10 :

The perimeter of a regular nonagon, or 9-gon, is 18 inches. Is this enough information to find the area? If so, find the area and explain your reasoning. If not, explain why not.

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