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Measurement Dilations and Measurements Proportions Geometric

Problem Solving

100 100 100 100

200 200 200 200

300 300 300 300

400 400 400 400

500 500 500 500

Final Jeopardy

Jeopardy BoardJeopardy Board

The net of a cylinder is shown below. Use the ruler on the Mathematics Chart to measure the dimensions of the cylinder to the nearest inch.

Board Answer

Measurement 100

1

8Which is closest to the total surface area of this cylinder?F 4 in.2

G 11 in.2

H 14 in.2

J 25 in.2

Board

Measurement 100The net of a cylinder is shown below. Use the ruler on the Mathematics Chart to measure the dimensions of the cylinder to the nearest inch. 1

8

Length _______3 in

Which is closest to the total surface area of this cylinder?F 4 in.2

G 11 in.2

H 14 in.2

J 25 in.2


8

Length _______

Width _______

3 in

4 in

Area = 12 in2 Lateral Area Only

Board


G 11 in.2

H 14 in.2

J 25 in.2


G 11 in.2

H 14 in.2

J 25 in.2

Board


8

Length _______

Width _______

3 in

4 in

Area = 12 in2 Lateral Area Only

Circles

Radius = ______

5

8As a decimal

Area of a circle = _______πr2

A = π(0.625)2

A = 1.227

Two CirclesTotal Surface

Area

12.0001.2271.227

14.454

Board Answer

Measurement 200The net of a cube is shown below. Use the ruler on the Mathematics Chart to measure the dimensions of the cube to the nearest inch.1

4Find the surface area of the cube to the nearest square inch.A 2 in.2

B 9 in.2

C 14 in.2

D 18 in.2

Board



B 9 in.2

C 14 in.2

D 18 in.2

1in

21

Board



B 9 in.2

C 14 in.2

D 18 in.2

1in

21

1in

21

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B 9 in.2

C 14 in.2

D 18 in.2

1in

21

1in

21

2.25 in2

2.25 in2 2.25 in2 2.25 in2 2.25 in2

2.25 in2

Board Answer

Measurement 300The net of a cylinder is shown below. Use the ruler on the Mathematics Chart to measure the dimensions of the cylinder to the nearest tenth of a centimeter.Find the total surface area of this cylinder to the nearest square centimeter.F 6 cm2

G 14 cm2

H 19 cm2

J 33 cm2

Board

Measurement 300The net of a cylinder is shown below. Use the ruler on the Mathematics Chart to measure the dimensions of the cylinder to the nearest tenth of a centimeter.Find the total surface area of this cylinder to the nearest square centimeter.F 6 cm2

G 14 cm2

H 19 cm2

J 33 cm2

9.4 cm

2 cm

1.5 cmRect. = 18.8 cm2

Circle = 7.1 cm2 Circle = 7.1 cm2

33.0 cm2

Board Answer

Measurement 400The net of a cylinder is shown below. Use the ruler on the Math Chart to measure the dimensions of the cylinder to the nearest tenth of a centimeter. Which of the following best represents the total surface area of this cylinder?F 142 cm2

G 93 cm2

H 23 cm2

J 14 cm2

The net of a cylinder is shown below. Use the ruler on the Math Chart to measure the dimensions of the cylinder to the nearest tenth of a centimeter. Which of the following best represents the total surface area of this cylinder?F 142 cm2

G 93 cm2

H 23 cm2

J 14 cm2

Board

Measurement 400

7 cm

10.5

cm

1.7 cm

Rect. = 73.5 cm2

Circle = 9.1 cm2 Circle = 9.1 cm2

91.7 cm2

Board Answer

Measurement 500Use the ruler on the Mathematics Chart to measure the dimensions of the composite figure to the nearest tenth of a centimeter.Which best represents the approximate area of this composite figure?A 34.7 cm2

B 38.8 cm2

C 44.6 cm2

D 54.5 cm2

Board

Measurement 500Use the ruler on the Mathematics Chart to measure the dimensions of the composite figure to the nearest tenth of a centimeter.Which best represents the approximate area of this composite figure?A 34.7 cm2

B 38.8 cm2

C 44.6 cm2

D 54.5 cm2 2.5 cm

3.3

cm

10.5 cm

3.4

cm

3.4 cm

Area of triangle = _____1

bh2

Area of rectangle = _____LW

Board Answer

The scale of two similar quadrilaterals is 1:2. The perimeter of the smaller quadrilateral is 80 centimeters. What is the perimeter of the larger quadrilateral?A 40 cmB 80 cmC 160 cmD 320 cm

Dilations and Measurements 100

The scale of two similar quadrilaterals is 1:2. The perimeter of the smaller quadrilateral is 80 centimeters. What is the perimeter of the larger quadrilateral?A 40 cmB 80 cmC 160 cmD 320 cm

Board


Pick a rectangle with a perimeter of 80 cm

30 cm

10 cm

Create a rectangle twice as big60 cm

20 cm

Perimeter = 160 cm

Area = 300 cm2

Area = 1200 cm2

The area is 4 times as big

Board Answer

Dilations and Measurements 200The scale factor of two similar polygons is 2:3. The perimeter of the larger polygon is 150 centimeters. What is the perimeter of the smaller polygon?A 100 cmB 75 cmC 50 cmD 150 cm

Board

Dilations and Measurements 200The scale factor of two similar polygons is 2:3. The perimeter of the larger polygon is 150 centimeters. What is the perimeter of the smaller polygon?A 100 cmB 75 cmC 50 cmD 150 cm

Pick a rectangle with a perimeter of 150 cm

60 cm

15 cm

Create a rectangle 2/3 as big40 cm

10 cmPerimeter = 100 cm

Area = 900 cm2

Area = 400 cm2

The area is as big4

9

Board Answer

Dilations and Measurements 300Tony and Edwin each built a rectangular garden. Tony’s garden is twice as long and twice as wide as Edwin’s garden. If the area of Edwin’s garden is 600 square feet, what is the area of Tony’s garden?A 1200 ft2

B 2400 ft2

C 3600 ft2

D 4800 ft2

Board

Dilations and Measurements 300Tony and Edwin each built a rectangular garden. Tony’s garden is twice as long and twice as wide as Edwin’s garden. If the area of Edwin’s garden is 600 square feet, what is the area of Tony’s garden?A 1200 ft2

B 2400 ft2

C 3600 ft2

D 4800 ft2

Pick a rectangle with an area of 600 ft2

30 ft

20 ft

Create a rectangle twice as big60 ft

40 ft

Area = 2400 ft2 (4 times the area)

Per. = 100 ft

Per. = 200 ftThe perimeter is twice as big

Board Answer

Dilations and Measurements 400A rectangular solid has a volume of 24 cubic decimeters. If the length, width, and height are all changed to their original size, what will be the new volume of the rectangular solid?A 3 dm3

B 4 dm3

C 6 dm3

D 12 dm3

1

2

Board

Dilations and Measurements 400A rectangular solid has a volume of 24 cubic decimeters. If the length, width, and height are all changed to their original size, what will be the new volume of the rectangular solid?A 3 dm3

B 4 dm3

C 6 dm3

D 12 dm3

1

2

Pick a rectangular solid with a volume of 24 dm3

6 dm

2 dm

Create a rectangle half as big

3 dm

1 dm Vol = 3 dm3 ( the volume)

2 dm

1 dm1

8

Board Answer

Dilations and Measurements 500If the surface area of a cube is increased by a factor of 4, what is the change in the length of the sides of the cube?F The length is 2 times the original length.

G The length is 4 times the original length.

H The length is 6 times the original length.

J The length is 8 times the original length.

If the surface area of a cube is increased by a factor of 4, what is the change in the length of the sides of the cube?F The length is 2 times the original length.

G The length is 4 times the original length.

H The length is 6 times the original length.

J The length is 8 times the original length.

Board


Each length 8 times as big makes the area _____ times bigger64




Board Answer

Proportions 100Kate has 2 similar triangular pieces of paper, as shown below.

Using the dimensions given, find the approximate length of the side labeled p.

Board

Proportions 100Kate has 2 similar triangular pieces of paper, as shown below.

F 2.4 centimetersG 7.3 centimetersH 16.5 centimetersJ 19.6 centimeters

Using the dimensions given, find the approximate length of the side labeled p.

left side

bottom18

12

p

11

18p = 132 18 18

x = 7.3

Board Answer

Proportions 200If ∆TSR is similar to ∆TNM, what is the length of x?

Board

Proportions 200If ∆TSR is similar to ∆TNM, what is the length of x?

A 240 unitsB 140 unitsC 120 unitsD 70 units

outside

diagonal70

120

240

x

18p = 132

120x = 16800 120 120

x = 140

Board Answer

Proportions 300A certain parallelogram has the dimensions shown. Which set of dimensions would produce a similar figure?F 17.6 cm, 88 cmG 70.4 cm, 176 cmH 105.6 cm, 132 cmJ 140.8 cm, 220 cm

Board

Proportions 300A certain parallelogram has the dimensions shown. Which set of dimensions would produce a similar figure?F 17.6 cm, 88 cmG 70.4 cm, 176 cmH 105.6 cm, 132 cmJ 140.8 cm, 220 cm

(35.2 cm, 44 cm) 2 = __________70.4, 88

(35.2 cm, 44 cm) 4 = __________140.8, 176

(35.2 cm, 44 cm) 3 = __________105.6, 132

Board Answer

Proportions 400To estimate the height of her school’s gym, Nicole sights the top of the gym wall in a mirror that she has placed on the ground. The mirror is 3.6 meters from the base of the gym wall. Nicole is standing 0.5 meter from the mirror, and her height is about 1.8 meters. What is the height of the gym wall?

Board

Proportions 400To estimate the height of her school’s gym, Nicole sights the top of the gym wall in a mirror that she has placed on the ground. The mirror is 3.6 meters from the base of the gym wall. Nicole is standing 0.5 meter from the mirror, and her height is about 1.8 meters. What is the height of the gym wall?

F 1 mG 5.9 mH 7.2 mJ 12.96 m

height

bottom1.8

0.5

3.6

x

0.5x = 6.48 0.5 0.5

x = 12.96

Board Answer

Proportions 500In El Paso, Texas, the streets named Hercules Avenue, Hondo Pass Drive, and Trans Mountain Road are parallel. They all intersect Dyer Street and U.S. Route 54, as shown on the map below.If all of these streets are straight line segments, how long is Dyer Street between Hercules Avenue and Trans Mountain Road?

Board

Proportions 500In El Paso, Texas, the streets named Hercules Avenue, Hondo Pass Drive, and Trans Mountain Road are parallel. They all intersect Dyer Street and U.S. Route 54, as shown on the map below.If all of these streets are straight line segments, how long is Dyer Street between Hercules Avenue and Trans Mountain Road?A 8,450 ftB 9,900 ftC 13,200 ftD 19,800 ft

left

right5280

6600

x

10560

5280x = 69696000 5280 5280

x = 13,200

Board Answer

Geometric Problem Solving 100The map below shows 2 different routes Ms. Bentsen can take to drive to the airport from her house.How many miles could Ms. Bentsen save by traveling on Airport Road instead of Mountain Highway and Oak Road to get to the airport?

Board

Geometric Problem Solving 100The map below shows 2 different routes Ms. Bentsen can take to drive to the airport from her house.How many miles could Ms. Bentsen save by traveling on Airport Road instead of Mountain Highway and Oak Road to get to the airport?A 20 miB 30 miC 35 miD 60 mi

a2 + b2 = c2

252 + b2 = 652

625 + b2 = 4225-625 -625

b2 = 3600b = 6060 mi

Distance = _____85 mi Distance saved = _____20 mi

Board Answer

Geometric Problem Solving 200The total area of trapezoid FGHJ is 52 square inches.What is the approximate length of FJ?

Board

Geometric Problem Solving 200The total area of trapezoid FGHJ is 52 square inches.What is the approximate length of FJ?

A 8.0 in.B 8.5 in.C 11.0 in.D 11.5 in.

a2 + b2 = c2

82 + 32 = c2

64 + 9 = c2

3 in

8 in

73 = c2

8.5 = c

Board Answer

Geometric Problem Solving 300What is the area of the square in the figure below?

Board

Geometric Problem Solving 300What is the area of the square in the figure below?

A 5.2 square unitsB 6.7 square unitsC 27 square unitsD 45 square units

3 in

6 in

a2 + b2 = c2

62 + 32 = c2

36 + 9 = c2

6.7 = c45 = c2

6.708 in

Area of a square ______s2

Board Answer

Geometric Problem Solving 400The shaded area in the circle below represents the section of a park used by the chamber of commerce for a fund-raising event.What is the approximate area of the section of the park used for the fund-raiser?

Board

Geometric Problem Solving 400The shaded area in the circle below represents the section of a park used by the chamber of commerce for a fund-raising event.What is the approximate area of the section of the park used for the fund-raiser?

F 339 square feetG 1,357 square feetH 4,071 square feetJ 12,214 square feet

2120(36)

360

Board Answer

Geometric Problem Solving 500A frozen dinner is divided into 3 sections on a circular plate with a 12-inch diameter.What is the approximate length of the arc of the section containing peas?

F 3 in.G 21 in.H 16 in.J 5 in.

Board

Geometric Problem Solving 500A frozen dinner is divided into 3 sections on a circular plate with a 12-inch diameter.What is the approximate length of the arc of the section containing peas?

52(12)

360

Final Jeopardy Category

Final Jeopardy Category

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Final Jeopardy QuestionFinal Jeopardy Question

Answer

In ∆STR, and are parallelQP TRIf SQ = 6 units, QT = 24 units, and the perimeter of ∆SQP is 20 units, what is the perimeter of ∆STR?

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Final Jeopardy AnswerFinal Jeopardy AnswerIn ∆STR, and are parallelQP TRIf SQ = 6 units, QT = 24 units, and the perimeter of ∆SQP is 20 units, what is the perimeter of ∆STR?

A 80 unitsB 100 unitsC 320 unitsD 500 units

6 24

How long is ST? _______30

How many times bigger is the larger triangle? _______5

The perimeter is how many times larger? _______5

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