Area of Regular Polygons Worksheet
Calculate the area of regular polygons using various formulas and properties, including apothem, side length, and perimeter.
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Area of Regular Polygons
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Read each question carefully and show all your work. Use the provided space for your answers. Round your answers to two decimal places where necessary.
1. Which of the following formulas is used to calculate the area of a regular polygon when the apothem (a) and perimeter (P) are known?
A = Pa
A = 2Pa
A = (1/2)Pa
A = P/a
2. What is the measure of each interior angle of a regular octagon?
90°
108°
135°
150°
3. The of a regular polygon is the distance from the center to the midpoint of a side.
4. A regular polygon with 6 equal sides and 6 equal angles is called a .
5. A regular hexagon has a side length of 8 cm. Calculate its area. (Hint: You may need to find the apothem first.)
6. A regular pentagon has an apothem of 6 cm and a side length of 8.71 cm. Find its perimeter and area.
7. All regular polygons can be inscribed in a circle.
True
False
8. The area of a regular polygon increases as the number of sides increases, assuming the perimeter remains constant.
True
False
Match the term on the left with its definition on the right.
9. Apothem
a. A polygon with all sides and all angles equal.
10. Regular Polygon
b. The sum of the lengths of all sides of a polygon.
11. Perimeter
c. The distance from the center of a regular polygon to the midpoint of a side.