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Worksheet: Areas of Regular Polygons

Q1:

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

  • A 751 cm2
  • B 994 cm2
  • C 1 395 cm2
  • D 497 cm2
  • E 262 cm2

Q2:

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

  • A 509 cm2
  • B 674 cm2
  • C 946 cm2
  • D 337 cm2
  • E 178 cm2

Q3:

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

Q4:

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

Q5:

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

Q6:

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

Q7:

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

Q8:

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

Q9:

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.

  • A 30 935 cm2
  • B 44 471 cm2
  • C 46 949 cm2
  • D 23 475 cm2

Q10:

Find the area of the shaded region rounded to the nearest tenth.

Q11:

Find the area of the shaded region rounded to the nearest tenth.

Q12:

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

Q13:

A flowerbed is designed as a regular hexagon with an area of 5 4 3 m2 . Find the side length of the hexagon giving the answer to the nearest meter.

  • A 3 m
  • B 4 m
  • C 7 m
  • D 6 m
  • E 5 m

Q14:

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

Q15:

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

Q16:

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

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?

Q19:

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

Q20:

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