Lesson Worksheet: Areas of Regular Polygons Mathematics

In this worksheet, we will practice finding areas of regular polygons given their side lengths using a formula.

Q1:

Find the area of a regular 14-sided polygon given the side length is 21 cm. Give the answer to two decimal places.

Q2:

The perimeter of a regular pentagon is 85 cm. Find the area giving the answer to the nearest square centimeter.

Q3:

Find the area of a regular hexagon with a side length of 35 cm giving the answer to two decimal places.

Q4:

The shown figure represents a circle inside a regular hexagon. Find the area of the shaded regions, giving your answer to the nearest tenth.

Q5:

The side of a regular octagon is 5 cm long. Find the area of the octagon giving the answer to two decimal places.

Q6:

The side length of a regular pentagon is 13 cm. Find the area of the pentagon giving the answer to three decimal places.

Q7:

A regular heptagon has a side length of 36 cm. Find the area giving the answer to two decimal places.

Q8:

Find the total area of the shaded regions in the regular polygons below, giving your answer to the nearest tenth.

Q9:

If four congruent triangles are cut off from the corners of the rectangle to make an octagon as shown, what is the area of the octagon?

Q10:

A regular octagon has a side length of 88 cm. Find the area giving the answer to two decimal places.

Q11:

The base of a fish tank is a regular pentagon with a side length of 189 cm. Find the area of the base to the nearest square centimeter.

Q12:

A flower bed is designed as a regular hexagon with an area of 543 m2. Find the side length of the hexagon giving the answer to the nearest meter.

Q13:

The perimeter of a regular pentagon is 70 cm. Find the area giving the answer to the nearest square centimeter.

Q14:

Find the area of a regular hexagon with a side length of 38 cm giving the answer to two decimal places.

Q15:

A regular heptagon has a side length of 89 cm. Find the area giving the answer to two decimal places.

Q16:

The side length of a regular pentagon is 6 cm. Find the area of the pentagon giving the answer to three decimal places.

Q17:

The side of a regular octagon is 11 cm long. Find the area of the octagon giving the answer to two decimal places.

Q18:

Find the area of a regular 15-sided polygon given the side length is 66 cm. Give the answer to two decimal places.

Q19:

Determine, to the nearest hundredth, the area of a regular hexagon whose circumcircle is 𝑥+𝑦14𝑥12𝑦+9=0.

Q20:

The area of a regular decagon is 155.8 cm2. What is the perimeter of the decagon rounded to one decimal place?

Q21:

Complete the following: The area of a regular octagon with perimeter 40 is .

  • A1054tan
  • B54tan
  • C8404tan
  • D854tan
  • E864tan

Q22:

Find the side length of a seven-sided regular polygon with an area of 817.63 cm2.

Q23:

Complete the following: The area of a regular polygon can be calculated using the formula 14𝑛𝑥, where 𝑛 is the number of sides and 𝑥 is the side length.

  • A𝜋𝑛
  • Bcot𝜋𝑛
  • Ctan𝜋
  • Dtan𝜋𝑛
  • Ecot𝜋

Q24:

Which of the following is the formula that is used to calculate the area of a regular 𝑛-sided polygon with side length 𝑥?

  • A𝑛𝑥4tan
  • B𝑛𝑥4cot
  • C𝑛𝑥2tan
  • D𝑛𝑥4𝜋tan
  • E𝑛𝑥4tan

Q25:

Which of the following is the area of a regular hexagon with a perimeter of 120 cm?

  • A6003 cm2
  • B1,2003 cm2
  • C2,4003 cm2
  • D303 cm2
  • E2003 cm2

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