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Unit 11

2-D & 3-D Figures

Name:

Teacher:

Grade:

1

2

LESSON 1 CLASSWORK

AREA OF 2D FIGURES

SHAPE PICTURE AREA FORMULA

3

12

3m 8m

FIND THE AREA OF EACH FIGURE:

1. 2.

8

10 16

3. 4.

4

20 20

9

5. 6.

9

9 15

Leave answer in terms of pi Round answer to the nearest tenth.

7) r = d = 8) r = d =

4

7

4

FIND THE MISSING DIMENSION, GIVEN THE AREA (SOLVE ALGEBRAICALLY):

9) THE AREA OF A SQUARE IS 400 SQUARE UNITS. WHAT IS THE DISTANCE OF EACH SIDE?

10) THE AREA OF A RECTANGLE IS 240 SQUARE UNITS. IF THE LENGTH OF THE RECTANGLE IS 24 UNITS, WHAT IS

THE WIDTH?

11) THE AREA OF A PARALLELOGRAM IS 54 SQUARE FEET. IF THE HEIGHT OF THIS FIGURE IS 9 FEET, HOW

LONG IS THE BASE?

12) A TRAPEZOID HAS AN AREA OF 240 SQUARE FEET. THE MEASURES OF THE BASES ARE 10 UNITS AND 16 UNITS,

RESPECTIVELY. WHAT IS THE HEIGHT OF THIS TRAPEZOID?

13) A TRIANGULAR MONUMENT IS BEING CONSTRUCTED IN A PARK. THE TOTAL AREA OF THE MONUMENT IS 280

SQUARE UNITS, AND THE BASE IS 28 FEET WIDE. HOW TALL IS THE MONUMENT?

14) A RECTANGULAR ROOM HAS AN AREA OF 600 SQUARE FEET. THE LENGTH OF THE ROOM IS 30 FEET, WHAT IS

THE WIDTH?

15) WHAT IS THE AREA OF A TRIANGLE WITH A HEIGHT OF 24 FEET AND A BASE OF 10 FEET?

5

1.2

LESSON 1 Classwork

AREA OF 2D FIGURES

Try these:

FIND THE AREA OF EACH FIGURE:

1. 2.

4

20 10

3. 4. ROUND TO THE NEAREST HUNDREDTH

2.5

5. 6.

90

90 12

FIND THE MISSING DIMENSION, GIVEN THE AREA (SOLVE ALGEBRAICALLY):

7. THE AREA OF A SQUARE IS 169 SQUARE UNITS. WHAT IS THE DISTANCE OF EACH SIDE?

8. THE AREA OF A RECTANGLE IS 120 SQUARE UNITS. IF THE LENGTH OF THE RECTANGLE IS 5 UNITS, WHAT IS THE

WIDTH?

11

8

5

6

6

LESSON 2 CLASSWORK

AREA OF COMPOSITE 2D FIGURES

Composite figure

Area = (in terms of pi)

Area =

(to the nearest tenth)

Area = (in terms of pi)

Area =

(to the nearest tenth)

3)

Area =

Examples

1)

2)

7

6)

4)

Area =

(to the nearest tenth)

5)

Area = Area = (in terms of pi)

7) 8)

Area =

Area =

8

LESSON 2 Classwork

AREA OF COMPOSITE 2D FIGURES

Try These:

1) 2)

Area = Area =

3)

Area = Area = (in terms of pi)

4)

9

Prism- two parallel, congruent faces called bases

Pyramid - one base that is a polygon and faces that are triangles.

NOT a pyramid or prism - has curved sides

Practice : Name each solid.

LESSON 3 CLASSWORK

NAMING 3D FIGURES

9)

10

1. Look at the 3-D shapes below. Write the name of each one and then list what 2D shapes you would need to make

each one. Ex) A Rectangular Prism needs 4 rectangles and 2 squares.

a b c d e f

2. Now match the correct net to the correct 3-D figure.

1.

Practice:

2. 3. 4. 5. 6.

1) 2) 3) 4)

5) 6) 7) 8)

11

Try these:

What are the names of the shapes below?

LESSON 3 Classwork

NAMING 3D FIGURES

1) 2) 3) 4)

6)

Identify the cross section

7) 8) 9)

Review

11) What is an equation of the line that passes through the point (4,- 6) and has a slope of - 3?

12) What is the value of the y-coordinate of the solution to the system of equations x + 2y = 9 and x - y = 3?

13) What is the product of 12 and 4.2 × 106

expressed in scientific notation?

14) Which expression represents in simplest form?

10)

5)

12

SURFACE AREA:

LESSON 4 CLASSWORK

SURFACE AREA

Jim and Kim want to wrap two presents. One is a cube and the other a rectangular prism.

How can they determine the amount of wrapping paper they will need?

12 in.

16 in.

2 in.

12 in.

5 in.

6 in.

Practice

1

13

1. 3cm

Surface Area

(to the nearest tenth)

8cm

2.

Surface Area

14

5m 4m

5m

12m

Find the surface area of each figure.

3) 4)

5) 6)

7)

10m

15

5i

3in

LESSON 4 Classwork

SURFACE AREA

Try These:

1)

a) What is the name of the 3D figure to the left?

b) Name the 2D shapes that make up this figure.

c) Find the surface area.

2)

n a) What is the name of the 3D figure to the left?

b) Name the 2D shapes that make up this figure.

10in

c) Find the surface area.

6in

3) Find the surface area rounded to the nearest hundredth.

15in

16

5

9

Volume – The measure of space a three-dimensional figure occupies.

Discover the formula:

LESSON 5 CLASSWORK

VOLUME

Imagine filling each figure with cubes or liquid. As you are filling the figure you will first cover the base of the figure.

Then you will continue filling it to the top.

Find the volumes of the figures below.

1)

5 in.

5 in.

5 in.

5 in.

in.

2) 3) 9 in.

6 in.

9 in.

in.

7 in. 5 in.

Base

17

6 in.

4) 5)

3 in.

4 in.

7)

6)

8)

18

Try These:

Find the volume of each of the following (round to the nearest tenth if necessary)

2)

4)

LESSON 5 Classwork

VOLUME

16m

5m 7m

5) The diameter of the igloo is 20 feet, find the volume.

1)

3)

19

LESSON 6 CLASSWORK

PRACTICE WITH SA AND VOLUME

Decide whether each question represents AREA, SA, or VOLUME. THEN SOLVE EACH PROBLEM.

1) A farmer needs want to fill his silo with grain to store for the winter. The height of the silo is 30 feel and its diameter

is 10 feet. How much grain can he store?

2) UPS requires that all boxes be shipped brown paper for mailing. If the box measures 3 feet by 3 feet by 2 feet, how

much of the brown paper do you need?

3) The school band is selling pennants. Each pennant is cut in the shape of a triangle 4 feet long and 1 foot high. How

many square feet of fabric are needed to make 200 pennants (assuming no waste)?

4) Soda is sold in aluminum cans that measure 6 inches in height and 2 inches in diameter. How many cubic inches

of soda are contained in a full can? (Round answer to the nearest tenth of a cubic inch.)

5) Sarah is going to Marilyn’s Sweet 16 and wants to wrap the rectangular gift box in a shiny red decorative paper. The

box is 9 inches long, 5 inches wide and 4 inches high. What is the minimum amount of decorative paper needed to cover

the box?

6) Lin is planting a circular garden of tulips. She plans to plant four different colors in equal amounts. The garden will

have a diameter of 24 feet. How many square feet, to the nearest foot, of space will she have for each of the colors?

20

30 95 24

27 58

Vocabulary:

LESSON 7 CLASSWORK

UNDERSTANDING SIMILAR TRIANGLES

Similar: Corresponding:

A

20 95 16

Two triangles are similar if:

N

C 27 58 B

28 P

42 O

1) List the angles which are corresponding 2) List the sides which are corresponding

a) A

b) B

c) C

a) AC corresponds to

b) AB corresponds to

c) BC corresponds to

3) Determine which sides are in proportion and PROVE that they are equal

a) 20

b)

30 24 28

20

c)

42 16

28 42

DETERMINING CORRESPONDING ANGLES:

4) If RST LMN, which of the following angles correspond with each other?

(hint: Mark all corresponding angles)

R a) R

N

c) L

b) N

d) S

Remember – In similar triangles corresponding angles are CONGRUENT!!

S T L M

2x + 3

x

U O

N

D

y 50

J 30 K

42

5) If DEF JKL, Which sides of the following triangles are corresponding?

(hint: Mark all corresponding sides)

E L J

F K

a) DE corresponds to

b) EF corresponds to

c) DF corresponds to

6) Complete the proportional equation to represent similarity from the triangles above.

a) 𝐷𝐸̅̅ ̅̅

𝐽𝐾̅̅̅̅=

𝐸𝐹̅̅ ̅̅ b)

𝐷𝐹̅̅ ̅̅

𝐷𝐸̅̅ ̅̅=

𝐽𝐾̅̅̅̅ c)

𝐾𝐿̅̅ ̅̅

𝐽𝐾̅̅̅̅=

𝐸𝐹̅̅ ̅̅

7) DEF JKL are similar, find the missing value

F x D a) Find x b) Find y

24

E L

8) If mK = 115 and mJ = 31, find the following angles

a) mL = b) mE = c) mD = d) mF =

9) RST LNM, determine the length of LM and NM given the following figure. L

R 25

M

T N 10

S

10) If STU MNO, which of the following angles correspond with each other?

M a) U b) S c) T

21

SIMILAR TRIANGLES HAVE SIDES THAT ARE IN PROPORTIONS. IF

TWO SETS OF SIDES ARE _ , THEN ALL THREE SIDES ARE !

S T

21

X M

A

D

x 12

D

LESSON 7 Classwork

UNDERSTANDING SIMILAR TRIANGLES

Try These:

1) If DAM XYZ, which of the following angles correspond with each other?

D a) A b) X c) Z

Y Z

2) Using the triangles above: If mD = 48 and mZ = 40, what is

a) mA = b) mX = c) mY =

3) If DEF JKL and KL = x + 6 ; DE = 8 ; JK = 4x and EF = 3; find the value of x.

E L J

F K

4) DEF JKL are similar, find the missing value

F 24 D J

y K

18 12

a) Find x b) Find y

E L

5) If DEF JKL and KL = 15 ; DE = 8 ; JK = 20 ; find EF

E L J

F K

6) BAC is similar to FTP. AC = 4 ; CB = 8 ; PF = 3x ; and TP = x + 4. Find PF and TP

22

__

__

_____________________________________________

LESSON 8 CLASSWORK

SLOPES AND SIMILAR TRIANGLES

If two right triangles are created on the same line, with

the hypotenuse on the line, they are then SIMILAR triangles

Parts of a right triangle

1) What is height of the large right triangle?

2) What is the base of the large right triangle?

3) What is the slope from the hypotenuse of the large

right triangle?

4) What is height of the small right triangle?

5) What is the base of the small right triangle?

6) What is the slope from the hypotenuse of the small

right triangle?

*** What do you observe?

ALL TRIANGLES CREATED ON THE SAME LINE

ARE BECAUSE OF THEIR SLOPES

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7. What is the slope of the line?

8. What is the y-intercept of the line?

9. What is the equation of the line?

10. What is the height of the big triangle?

What is the base of the big triangle?

11. Is there a relationship between the height and base of

the big triangle?

12. If the small triangle has a base of 4, what is

the height?

13. The figure to the right is a coordinate plane with a

line and two triangles. If the triangles both have their

hypotenuse on the line, determine the following.

a. What is the value of k?

b. What is the equation of the line?

14. Two right triangles are drawn on a coordinate plane.

Triangle ABC Triangle FGH

A(-8, 6) B(-8,2) C(-2, 6) F(-4, 3) G(-4,1) H(-1, 3)

a. Are these triangle similar?

Y

(k,8)

(4,5)

(0,3)

X

24

LESSON 8 Classwork

SLOPES AND SIMILAR TRIANGLES

Try These:

1. What is the slope of the line?

2. What is the y-intercept of the line?

3. What is the equation of the line?

4. What is the height of the big triangle? _

What is the base of the big triangle?

5. Is there a relationship between the height and base of

the big triangle?

6. If the small triangle has a base of 5, what is

the height?

7. In the coordinate plane shown, there are two overlapping

triangles (I and II). Triangle I and Triangle II are similar

a. What is the equation of the line drawn?

Y

(0,9)

b. What is the value of c in the coordinate (c, 6)?

(0,6)

I

(c,6)

II

(6,0) X

8. Graph the two right triangles on a coordinate plane.

Triangle ABC Triangle FGH

A(9, -8) B(1, 0) C(1, -8) F(6, 3) G(2,7) H(2, 3)

a. Are these triangle similar?