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1 Name the regular polygon shown below.

2 Name the regular polygon shown below.

3 Determine the sum of the interior angles of a decagon.

4 Determine the sum of the interior angles of the polygon shown below.

5 Which regular polygon has interior angles that measures 90° each?

6 Which regular polygon has interior angles that measures 135° each?

7 How many sides does a polygon have if the sum of the interior angles is 360°?

8 How many sides does a polygon have if the sum of the interior angles is 1080°?

9 Given the regular polygon below, determine the value of x.

10 Given the regular polygon below, determine the value of x.

1 Definitions for Regular Polygons EVALUATED

Skill Builder: Definitions for Regular Polygons 357

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358 Chapter 11: Circles and Regular Polygons

1 In the regular polygon given below, identify the line segment passing through it.

2 In the regular polygon given below, identify the line segment that starts at the center of the polygon and ends at one of its sides making a 90 degree angle with that side.

3 How many diagonals can be drawn from vertex A in the regular pentagon below?

A

4 How many diagonals can be drawn from vertex A in the regular octagon below?

A

5 How many congruent isosceles triangles fit into a regular pentagon?

6 How many congruent isosceles triangles fit into a regular hexagon?

7 Determine the angle measures of the 4 congruent triangles that fit into a square.

8 Determine the angle measures of the 5 congruent triangles that fit into a regular pentagon.

9 Construct a regular pentagon with sides measuring 2cm each by using a ruler and a protractor.

10 Construct a regular hexagon with sides measuring 3cm each by using a ruler and a protractor.

2 Special Lines and Constructions of Regular Polygons EVALUATED

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Skill Builder: The Metric System - One Dimensional Conversions 359

1 Perform the following metric conversion.

39 ?cm dm=


422 ?m km=


5 ?m cm=


?23dam mm=


?0.751km dam=


0.0851 ?m mm=


?0.321cm m=


0.00281 ?m km=

9 Calculate the following sum and state your answer in m.

428 377 ?cm dm+ =

My Calculations

10 Calculate the following sum and state your answer in dm.

0.00825 48 ?0.km m+ =

My Calculations

3 The Metric System - One Dimensional Conversions

EVALUATED

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1 An equilateral triangle has a side length of 4cm. Calculate the triangle’s perimeter.

2 The perimeter of the equilateral triangle given below is 36cm. Determine the value of x.

3 A square has a side length of 5cm. Calculate the square’s perimeter.

4 Calculate the perimeter of the square given below.

5 A regular pentagon has a side length of 9cm. Calculate the pentagon’s perimeter.

6 The perimeter of the regular pentagon given below is 60cm. Determine the value of x.

7 Calculate the perimeter of the regular hexagon given below.

8 A regular hexagon has a side length of 8cm. Calculate the hexagon’s perimeter.

9 Calculate the perimeter of the regular octagon given below.

10 The perimeter of the regular octagon given below is 40cm. Determine the value of x.

4 The Perimeter of a Regular Polygon EVALUATED

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Skill Builder: The Metric System - Two Dimensional Conversions 361


2 28 ?1 dm m=

My Calculations


2 2285 ?3 dam km=

My Calculations


2 23 ?6 m mm=

My Calculations


2 22 ?hm m=

My Calculations


2 24 8 7 ?. 2 m dm=

My Calculations


2 20.0123 ?mm m=

My Calculations

5 The Metric System - Two Dimensional Conversions

EVALUATED

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7 Calculate the following sum and state your answer in m2.

2 20.718 0.0357 ?1dam hm+ =

My Calculations

8 Calculate the following sum and state your answer in dm2.

2 252500 8 ?45mm cm+ =

My Calculations

9 Calculate the following product and state your answer in m2.

.28 435 ?0 dam dm× =

My Calculations

10 Calculate the following product and state your answer in cm2.

0.0015 0.12 ?m dm× =

My Calculations

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Skill Builder: The Area of a Regular Polygon 363

1 A regular hexagon has a perimeter of 18cm and an apothem of 2.5cm. Calculate the hexagon’s area.

My Calculations

2 A regular octagon has a perimeter of 80cm and an apothem of 12cm. Calculate the octagon’s area.

My Calculations

3 Calculate the area of the regular pentagon given below.

My Calculations

4 Calculate the area of the regular octagon given below.

My Calculations

5 A regular hexagon has a side length of 12cm and an apothem of 10cm. Calculate the hexagon’s area.

My Calculations

6 A regular pentagon has a side length of 9cm and an apothem of 6cm. Calculate the pentagon’s area.

My Calculations

6 The Area of a Regular Polygon EVALUATED

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7 Calculate the perimeter of the regular hexagon given below.

Area = 1440cm2

My Calculations

8 Calculate the perimeter of the regular octagon given below.

Area = 30cm2

My Calculations

9 Calculate the apothem of the regular pentagon given below.

Area = 375cm2

My Calculations

10 Calculate the apothem of the regular octagon given below.

Area = 270cm2

My Calculations

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Skill Builder: Perimeters and Areas of Composite Figures 365

1 Calculate the perimeter of the composite shape.

My Calculations

2 Calculate the perimeter of the composite shape.

My Calculations

3 Calculate the perimeter of the shape.

My Calculations

4 Calculate the perimeter of the shape.

My Calculations

7 Perimeters and Areas of Composite Figures EVALUATED

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5 Calculate the area of the shape.

My Calculations


My Calculations


My Calculations

8 Calculate the area of the composite shape.

My Calculations

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Skill Builder: Perimeters and Areas of Composite Figures 367

9 Kevin is building a fence around the pool area at a hotel. To help Kevin figure out how much fencing to buy, calculate the perimeter of the shape.

My Calculations

10 Hillary is designing a floor plan for a new building. She needs to determine how much flooring to purchase. Help Hillary by calculating the area of the floor.

My Calculations

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1 Calculate the perimeter of the regular polygon that has an interior angle that measures 144°, and a side that measures 6cm.

My Calculations

2 Calculate the perimeter of the regular polygon that has an interior angle that measures 90°, and a side that measures 7cm.

My Calculations

3 What is the perimeter of the regular polygon whose sum of interior angles is 540° and whose side length is 9cm?

My Calculations

4 What is the perimeter of the regular polygon whose sum of interior angles is 1080° and whose side length is 4cm?

My Calculations

5 Calculate the unknown length x in the regular pentagon given below.

Area = 240cm2

My Calculations

8 Word Problems for Regular Polygons EVALUATED

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6 Calculate the unknown length x in the regular hexagon given below.

Area = 1440cm2

My Calculations

7 Calculate the area of the regular polygon whose apothem measures 4cm, one of whose sides measures 6cm, and one of whose interior angles is 108°.

My Calculations

8 Calculate the area of the regular polygon whose apothem measures 12cm. One of the sides of the regular polygon measures 10cm and one of the interior angles is 135°.

My Calculations

9 A garden in the shape of a regular hexagon with a side length of 5m is made on a square piece of land with a side length of 15m. The apothem of the regular hexagon measures 4.3m. What is the area of land that is not taken up by the garden?

My Calculations

10 The area of a swimming pool in the shape of a regular pentagon is 120m2. The distance from the middle of the pool to one of the sides is 6m. How much would it cost to paint the outer edge of the top of the pool if it costs $0.50 per metre?

My Calculations

Skill Builder: Word Problems for Regular Polygons 369

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1 Find the diameter and radius of each circle.

a. Black Circle

b. Red Circle

c. Green Circle

2 Find the diameter and radius of each circle.

a. Black Circle

b. Red Circle

c. Green Circle

3 Find the circumference of each circle rounded to the nearest tenth of a centimetre.

a. Black Circle

b. Red Circle

c. Green Circle

4 Find the circumference of each circle rounded to the nearest tenth of a centimetre.

a. Black Circle

b. Red Circle

c. Green Circle

9 Properties of Circles EVALUATED

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5 Calculate the circumference of the circle and length of the arc.

My Calculations

6 Calculate the circumference of the circle and the length of the arc.

My Calculations

7 Use a 180° protractor to measure the central angle. Then calculate the opposite angle.

8 Use a 180° protractor to measure the central angle. Then calculate the opposite angle.

9 Find the perimeter of the combined object.

10 Find the perimeter of the combined object.

Skill Builder: Properties of Circles 371

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1 The centre circle on a soccer field has a radius of 9.15 m. Draw a model of the centre circle using a scale factor of 1 cm = 2 m.

2 The wall clock in a Mathematics classroom has a radius of 20 cm. Draw a model of the wall clock using a 1:5 scale.

10 Constructing a Circle EVALUATED

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3 The symbol of the Olympic Games is composed of five interlocking circles coloured blue, yellow, black, green and red on a white background. Draw the symbol using the coordinates in the table below.

Circle Colour CentrePoint on

Circle

blue (–4, 2) (–6, 2)

black (0, 2) (0, 4)

red (4, 2) (6, 2)

yellow (–2, 0) (–2, –2)

green (2, 0) (2, –2)

4 Draw three collinear points: A, B and C, 3 cm apart. Draw a circle with its centre at A and its edge at B. Draw another circle with its centre at B and its edge at C. Draw a final circle with its centre at C and its edge at B. The circles provide a template for drawing a regular hexagon. Draw the hexagon.

Skill Builder: Constructing a Circle 373

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5 Make the following construction.

• Using a Cartesian graph, construct a square with vertices at (0, 4), (4, 0), (0, –4) and (–4, 0).

• Draw 4 circles with the centres at the vertices of the square and the edges at the origin (0, 0).

• Create a point at each intersection of a circle with a side of the square. There should be 8 all together.

• Draw line segments connecting the 8 points.

• You should have a regular octagon.

6 In Chinese philosophy, the concept of yin-yang has a familiar symbol. To draw it, follow these instructions.

• Using a Cartesian graph, construct a circle with its centre at (0, 0) and its edge at (0, 6).

• Draw a semicircle in the first quadrant with a centre at (0, 3) and an edge at (0, 0).

• Draw another semicircle in the third quadrant with a centre at (0, –3) and an edge at (0, 0).

• Draw 2 circles centred at (0, 3) and (0, –3) each with a radius of 1 unit.

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7 Which set of lines (black or blue) are used to find the centre of the circle that contains points A, B and C.

C B

A

C B

A

8 Use perpendicular bisectors to prove that point X is the centre of the circle that contains points A, B and C.

A C

X

B

9 A hockey team has a power play scheme where Brendan, Lars and Max are positioned at points on an imaginary circle.

The two defensemen, should be positioned on the blue line and also on the imaginary circle.

Find the imaginary circle, then place an X where each defenseman’s position should be.

Skill Builder: Constructing a Circle 375

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10 A carpenter finds the centre of a circular table using a framing square. Here are the steps.

Mark the edge.

Measure out 24 inches and place another mark, then draw a line connecting the marks. Repeat on the other side.

Measure out 12 inches on one line, then draw a line square to it. Repeat on the other side.

The centre of the table is where the lines cross.

Watch the video version of this question and explain how this is the same process as using perpendicular bisectors.

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1 Calculate the circumference of the following circle.

diameter = 7cm


diameter = 20cm



5 What is the diameter of the circle below if it has a circumference of 18.84cm?

6 What is the diameter of the circle below if it has a circumference of 25.12cm?

11 The Circumference of a Circle EVALUATED

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Skill Builder: The Circumference of a Circle 381

7 What is the radius of the circle below if it has a circumference of 37.68cm?

8 What is the radius of the circle below if it has a circumference of 31.4cm?

9 Calculate the perimeter of the following shape.

10 Calculate the perimeter of the following shape.

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1 If the circumference of the circle below is 75.36cm, calculate mAB.

My Calculations

2 If the circumference of the circle below is 50.24cm, calculate mAB.

My Calculations

3 If 18.5=mAB cm in the circle below, what is the circumference of this circle?

My Calculations

4 If 25.12=mAB cm in the circle below, what is the circumference of this circle?

My Calculations

12 Arc Length of a Circle EVALUATED

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5 Calculate mAB for the following circle.

My Calculations

6 Calculate mAB for the following circle.

My Calculations

7 If 47.1=mAB cm in the circle below, what is the radius of this circle?

My Calculations

8 If 19.625=mAB cm in the circle below, what is the radius of this circle?

My Calculations

Skill Builder: Arc Length of a Circle 383

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9 Given the circle below, calculate mBCA.

My Calculations

10 If 31.4=mBCA cm, calculate mAB in the circle below.

My Calculations

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1 Calculate the area of the circle given below.

My Calculations


My Calculations


diameter = 24cmDiameter = 24cm

My Calculations


diameter = 4cmDiameter = 4cm

My Calculations

13 The Area of a Circle EVALUATED

Skill Builder: The Area of a Circle 385

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5 Determine the radius of the circle given below whose area is 28.26cm2.

My Calculations

6 Determine the radius of the circle given below whose area is 50.24 cm2.

My Calculations

7 Determine the diameter of the circle given below whose area is 706.5cm2.

My Calculations

8 Determine the diameter of the circle given below whose area is 314cm2.

My Calculations

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9 Calculate the area of the shaded region in the diagram below.

•

11 cm

6 cm

My Calculations

10 Calculate the area of the shaded region in the diagram below.

3 cm

4 cm2 cm

My Calculations

Skill Builder: The Area of a Circle 387

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1 Given the circle and the information below, calculate .∠m AOB

A Circle = 254.34 cm2

A AOB = 84.78 cm2

A B

O•?

My Calculations

2 Given the circle and the information below, calculate .∠m AOB

A Circle = 452.16cm2

A AOB = 75.36cm2

My Calculations

3 Given the information in the circle below, calculate the area of sector AOB.

AB

O•

6 cm 150°

My Calculations

4 Given the information in the circle below, calculate the area of sector AOB.

AO

B

mAB = 20 cm

•

My Calculations

14 Area of a Circular Sector EVALUATED

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5 Calculate the area of the following shape.

My Calculations

6 Calculate the area of the following shape.

My Calculations

7 Given the circle and the information below, calculate the area of the circle.

A AOB = 4.71cm2

A

B

60° •O

My Calculations

8 Given the circle and the information below, calculate the area of the circle.

A

B

120°•O A AOB = 37.68cm2

My Calculations

Skill Builder: Area of a Circular Sector 389

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9 Given the circle and the information below, calculate the radius of the circle.

A AOB = 4.71cm2

A

B

60°•O

My Calculations

10 Given the circle and the information below, calculate the radius of the circle.

A

B

120°• O A AOB = 37.68cm2

My Calculations

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1 Given that the circumference of the circle below is 12.56cm, what is the circle’s area?

My Calculations

2 Given that the circumference of the circle below is 43.96cm, what is the circle’s area?

My Calculations

3 Given that the area of the circle below is 50.24cm2, what is the circle’s circumference?

My Calculations

4 Given that the area of the circle below is 78.5cm2, what is the circle’s circumference?

My Calculations

15 Word Problems for Circles Putting it all Together EVALUATED

Skill Builder: Word Problems for Circles Putting it all Together 391

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5 Given that the area of the shape below is 157cm2, what is the shape’s perimeter?

O•

180°

My Calculations

6 Given that the area of the shape below is 84.78cm2, what is the shape’s perimeter?

120°

My Calculations

7 Given that 15.7=mAB cm, calculate the area of the circular sector AOB.

A

B

O15.7cm60°

•

My Calculations

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Skill Builder: Word Problems for Circles Putting it all Together 393

8 Given that 39.25=mAB cm, calculate the area of the circular sector AOB.

A B

O•150°

39.25cm

My Calculations

9 Calculate the area of the shaded region in the shape below.

My Calculations

10 Calculate the area of the shaded region in the shape below.

My Calculations

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