Regular Polygons: Perimeter & Angle Calculations

Grade 9th

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| By Thames

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| Questions: 20 | Updated: Nov 21, 2025

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1) The central angle of a regular 18-gon is

10°

15°

20°

30°

The central angle of a regular polygon can be calculated using the formula: Central Angle = 360° / n, where n is the number of sides. For an 18-gon, this becomes 360° / 18 = 20°.

Explanation

The central angle of a regular polygon can be calculated using the formula: Central Angle = 360° / n, where n is the number of sides. For an 18-gon, this becomes 360° / 18 = 20°.

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About This Quiz

Regular Polygons: Perimeter & Angle Calculations - Quiz

Let's put your polygon skills to work with real measurements! In this quiz, you’ll find the perimeter, angles, and even areas of regular polygons used in signs, patios, gardens, and walkways. You’ll practice with triangles, squares, hexagons, and octagons while applying simple formulas step by step. By the end, you’ll... see moresee how math makes it easy to measure and design with polygons.
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2) A regular polygon has 15 sides. The measure of each interior angle is

150°

156°

160°

162°

To find the measure of each interior angle of a polygon, use the formula (n-2) × 180° / n, where n is the number of sides. For a polygon with 15 sides, the calculation is (15-2) × 180° / 15 = 156°.

Explanation

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3) A regular polygon has each exterior angle 30°. How many sides does it have?

The sum of the exterior angles of any polygon is 360 degrees. To find the number of sides, divide 360 by the measure of each exterior angle: 360° / 30° = 12. Therefore, the polygon has 12 sides.

Explanation

The sum of the exterior angles of any polygon is 360 degrees. To find the number of sides, divide 360 by the measure of each exterior angle: 360° / 30° = 12. Therefore, the polygon has 12 sides.

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4) A garden path is shaped as a regular hexagon with side 5 m. What is the walking distance around it?

20 m

25 m

30 m

35 m

The walking distance around a regular hexagon is the perimeter, which is calculated by multiplying the length of one side by the total number of sides (6). Hence, 5 m * 6 = 30 m.

Explanation

The walking distance around a regular hexagon is the perimeter, which is calculated by multiplying the length of one side by the total number of sides (6). Hence, 5 m * 6 = 30 m.

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5) A regular polygon has 18 sides. Each central angle equals

15°

18°

20°

24°

To find the central angle of a regular polygon, you can use the formula: Central Angle = 360° / number of sides. For an 18-sided polygon, the central angle is 360° / 18 = 20°.

Explanation

To find the central angle of a regular polygon, you can use the formula: Central Angle = 360° / number of sides. For an 18-sided polygon, the central angle is 360° / 18 = 20°.

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6) A square patio has a perimeter of 40 ft. Its area is

80 ft²

100 ft²

200 ft²

400 ft²

To find the area of the square, first calculate the side length from the perimeter. The perimeter is 4 times the side length, so the side length is 40 ft / 4 = 10 ft. The area is then the side length squared, which is 10 ft × 10 ft = 100 ft².

Explanation

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7) Each interior angle of a regular hexagon is

100°

110°

120°

135°

In a regular hexagon, the sum of the interior angles is (n-2) × 180° where n is the number of sides. For a hexagon, n = 6, so the sum is (6-2) × 180° = 720°. Since there are 6 angles, each interior angle is 720° ÷ 6 = 120°.

Explanation

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8) A square sandbox has side 8 m. The length of fencing needed is

16 m

24 m

32 m

64 m

To find the length of fencing needed for a square sandbox, calculate the perimeter using the formula: Perimeter = 4 × side length. Here, 4 × 8 m = 32 m.

Explanation

To find the length of fencing needed for a square sandbox, calculate the perimeter using the formula: Perimeter = 4 × side length. Here, 4 × 8 m = 32 m.

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9) A regular polygon has each interior angle 135°. How many sides does it have?

To find the number of sides (n) of a regular polygon given the measure of each interior angle, you can use the formula: Interior angle = (n - 2) * 180° / n. Setting the interior angle to 135° and solving for n gives n = 8, indicating the polygon is an octagon.

Explanation

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10) A triangular yield sign has a side length of 90 cm. Its perimeter is

180 cm

200 cm

240 cm

270 cm

The perimeter of an equilateral triangle is calculated by multiplying the side length by 3. Therefore, 90 cm * 3 = 270 cm.

Explanation

The perimeter of an equilateral triangle is calculated by multiplying the side length by 3. Therefore, 90 cm * 3 = 270 cm.

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11) A regular pentagon has side 12. What is its perimeter?

The perimeter of a polygon is calculated by multiplying the length of one side by the number of sides. A regular pentagon has 5 sides, so the perimeter is 12 × 5 = 60.

Explanation

The perimeter of a polygon is calculated by multiplying the length of one side by the number of sides. A regular pentagon has 5 sides, so the perimeter is 12 × 5 = 60.

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12) A regular octagon has perimeter 80. What is the length of each side?

A regular octagon has 8 equal sides. To find the length of each side, divide the perimeter by the number of sides: 80 ÷ 8 = 10.

Explanation

A regular octagon has 8 equal sides. To find the length of each side, divide the perimeter by the number of sides: 80 ÷ 8 = 10.

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13) A square has area 49 m². Each side is

5 m

6 m

7 m

8 m

The area of a square is calculated by squaring the length of one side. Since the area is 49 m², the side length is √49, which equals 7 m.

Explanation

The area of a square is calculated by squaring the length of one side. Since the area is 49 m², the side length is √49, which equals 7 m.

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14) A regular hexagon with apothem 8 and perimeter 48 has an area of

144

192

384

The area of a regular hexagon can be calculated using the formula: Area = (Perimeter × Apothem) / 2. Given the perimeter is 48 and the apothem is 8, the area equals (48 × 8) / 2 = 192.

Explanation

The area of a regular hexagon can be calculated using the formula: Area = (Perimeter × Apothem) / 2. Given the perimeter is 48 and the apothem is 8, the area equals (48 × 8) / 2 = 192.

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15) A triangular flower bed is equilateral with side 12 ft. The distance around it is

24 ft

30 ft

40 ft

36 ft

The perimeter of an equilateral triangle is calculated by multiplying the length of one side by three. Therefore, for a triangle with each side measuring 12 ft, the perimeter is 12 ft x 3 = 36 ft.

Explanation

The perimeter of an equilateral triangle is calculated by multiplying the length of one side by three. Therefore, for a triangle with each side measuring 12 ft, the perimeter is 12 ft x 3 = 36 ft.

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16) A regular octagon is inscribed in a circle of radius 10. What is each central angle?

45°

40°

36°

60°

The central angle of a regular octagon can be calculated using the formula 360° divided by the number of sides. Since an octagon has 8 sides, the central angle is 360° / 8 = 45°.

Explanation

The central angle of a regular octagon can be calculated using the formula 360° divided by the number of sides. Since an octagon has 8 sides, the central angle is 360° / 8 = 45°.

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17) A stop sign is a regular octagon with a side length of 30 cm. Its perimeter is

180 cm

210 cm

240 cm

300 cm

To find the perimeter of a regular octagon, you can use the formula: Perimeter = number of sides × length of one side. For a regular octagon, there are 8 sides. Thus, the perimeter is 8 × 30 cm = 240 cm.

Explanation

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18) A regular hexagon has side length 10. What is its perimeter?

The perimeter of a hexagon is calculated by multiplying the length of one side by the total number of sides. A hexagon has 6 sides, so the perimeter is 10 (side length) x 6 = 60.

Explanation

The perimeter of a hexagon is calculated by multiplying the length of one side by the total number of sides. A hexagon has 6 sides, so the perimeter is 10 (side length) x 6 = 60.

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19) A regular decagon has a side length of 6. Its perimeter is

120

A regular decagon has 10 sides. The perimeter is calculated by multiplying the side length by the number of sides: 6 * 10 = 60.

Explanation

A regular decagon has 10 sides. The perimeter is calculated by multiplying the side length by the number of sides: 6 * 10 = 60.

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20) A regular polygon has 9 sides. Each exterior angle measures

30°

40°

80°

90°

The measure of each exterior angle of a regular polygon can be calculated using the formula 360° divided by the number of sides. For a polygon with 9 sides, each exterior angle measures 360° / 9 = 40°.

Explanation

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