Mr.DeMeo - HOMEWORK



7ACC

Unit 11

2-D Figures

| |Date |Lesson |Topic |

| | |1 |Area of Triangles & Quadrilaterals |

| | |2 |Similar Figures with Perimeter and Area |

| | |3 |Finding Area of Circles |

| | |4 |Finding Circumference of Circles |

| | |5 |Area vs. Circumference |

| | | |Review |

| | | |Test |

| | | | |

Lesson 1

Area of Triangles & Quadrilaterals

Types of Triangles:

|Name of Triangle |Definition/Picture |Name of Triangle |Definition/Picture |

|Acute Triangle | |Scalene Triangle | |

|Right Triangle | |Isosceles Triangle | |

|Obtuse Triangle | | Equilateral | |

| | |Triangle | |

The sum of the measures of the angles of any triangle is ________________________

Classifying Quadrilaterals

A parallelogram is ________________________________________

________________________________________________________

________________________________________________________

A rectangle is ____________________________________________

________________________________________________________

A rhombus is ____________________________________________

________________________________________________________

A square is _______________________________________________

_________________________________________________________

A trapezoid is ___________________________________________

________________________________________________________

The sum of the measures of the angles of any quadrilateral is ________________________

Area Formulas of Triangles and Quadrilaterals

Definitions:

Area is _____________________________________

Altitude is __________________________________

• An altitude is needed when a figure doesn’t have a side with a 90[pic] angle.

A composite figure is made up of two or more shapes.

To find the area of a composite figure, decompose the figure into shapes with areas you know. Then find the sum of these areas.

~ When finding the Area of a figure always Square your units. ~

Shape Picture Area Formula

Find the Area of each figure:

1. 2.

3. 4.

5. 6.

7. Find the area of the following composite figures.

5m 5m Figure 1 Figure 2 Total

12m 2m

Find the missing dimension, given the area (solve algebraically):

8. The area of a square is 400 square units. What is the distance of each side?

9. The area of a rectangle is 240 square units. If the length of the rectangle is 24 units, what is the width?

10. The area of a parallelogram is 54 square feet. If the height of this figure is 9 feet, how

long is the base?

11. 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?

12. 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?

13. A rectangular room has an area of 600 square feet. The length of the room is 30 feet, what is the width?

14. What is the area of a triangle with a height of 24 feet and a base of 10 feet?

15. James is comparing the dimensions of a triangle and a rectangle. The two shapes have the same area. The height of the triangle is 20 feet, and the length of the rectangle is also 20. If the width of the rectangle is 40 feet, what must the base of the triangle be?

Lesson 1 – Homework

Find the Area of each figure:

1. 2.

3. 4.

5. 6.

7. Find the area of the composite figure

4cm Figure 1 Figure 2 Total

6cm

Find the missing dimension, given the area (solve algebraically):

8. The area of a square is 169 square units. What is the distance of each side?

1. The area of a rectangle is 120 square units. If the length of the rectangle is 5 units, what is the width?

Lesson 2

Similar Figures

Vocabulary

Congruent figures: Same shape, same size

Similar figures: Same shape, but NOT necessarily the same size

Corresponding: _____________________________________________________________________

For this reason, all congruent figures are similar, but not all similar figures are congruent.

Similar Figures have the following properties:

• Their corresponding sides have proportional lengths.

• Their corresponding angles are congruent.

Steps to finding the Perimeter or Area of Similar Figures:

• Always find the missing side first. (Set up a proportion to find missing side)

• Once all sides are present, use the correct formula to find perimeter/ area.

Examples

*Angles are congruent since all

5cm 2.5cm rectangles have four right angles.

7.5cm 3.75cm

The ratios of the lengths and widths of the rectangles are in proportion.

[pic] = [pic] (Cross multiply) *Therefore, the rectangles are similar because,

the rectangles have congruent angles and

18.75 = 18.75 corresponding sides are in proportion.

State whether the following are Similar Figures or Not.

1) 2) 8in

6m

1.5m 12in 16i n

4m 1m 3in

The following figures are similar. Find the missing side.

3) 4)

8m 4m 10cm 6cm x

5cm

10m x

Find the perimeter of each of the following similar figures.

5) 6)

14m 14m

7m 7m 1.5m x

10m x 2m 4m

Find the area of each of the following similar figures.

7) 8)

15m 2m 3cm 15cm

30m x 4cm x

Try These

1) A gate is 3 feet and casts a shadow 5 feet long. At the same time, a nearby building casts a shadow

45 feet long. What is the height of the building?

A. 15 feet B. 27 feet C. 43 feet D. 75 feet

2) Which describes these two figures?

A. Congruent but not similar

B. Neither similar nor congruent

4m 3m C. Similar but not congruent

D. Similar and congruent

6m 4.5m

3) The following right triangles are similar. Find the length for the side representing x.

A. 72 cm

B. 78 cm

C. 128 cm

96 cm 104cm x D. 139 cm

40cm 30cm

4) Justin has two rectangular photo prints that are similar. The length of the smaller print is 5 inches

and the width is 3 inches. The length of the larger print is 20 inches.

a) Find the width of the larger print.

b) Find the perimeter of the smaller print.

c) Find the Area of the larger print.

5) The ratio of the corresponding sides of two similar triangles is 4:9. The sides of the smaller

triangle are 10cm, 16cm, and 18cm.

a) Find the three dimensions of the larger triangle.

b) Find the perimeter of the larger triangle

Lesson 2 – Homework (2 pages)

Determine if the following polygons are similar or not similar:

1. 2.

12.5m

3.1m 8m 20m

7.5m 2m 3m 7.5m

Each pair of figures below is similar. Find the value of each variable.

3. 4. 12m n

30m 54m 6m 3m

45m y

5. A woman is 5 ft. tall and her shadow is 4 ft. long. A nearby tree has a shadow 30 ft. long. How tall

is the tree?

6. Paula casts a shadow 2 meters long at the same time a tree casts a shadow 28 meters long. The tree

is 17.5 meters tall. How tall is Paula?

7. ABC is similar to PQR. Find each measure.

C R 1) Length of AB

21 ft 14 ft 2) Length of RP

16.8 ft 3) Measure of [pic]A

53[pic] B 92[pic] Q 4) Measure of [pic]Q

A P 8 ft

8. An image is 16 in. by 20 in. You want to make a copy that is similar. Its longer side will be 38 in.

The copy costs $0.60 per square inch. Estimate the copy’s total cost.

9. You want to enlarge a copy of the flag of the Philippines that is 4 in. by 8 in. The two flags will be

similar. How long should you make the shorter side if the long side is 24 ft.?

Find the Perimeter of each figure. Find the Area of each figure

10. 11.

x 4cm

6m 9m

8m x 12.5cm 5cm

Review

12. 5x – 9 + 10 = 31 13. -2(4x + 9) = 30 14. 8x – 10x + 8 = -20

Simplify:

15. 4x + 2(3x + 4) 16. – 5(x – 8) – 12 17. (4x – 4)[pic] + 4x – 3

Factor:

18. 12x + 16 19. 15x + 30 20. 18x – 45

Lesson 3

Finding Area of a Circle

Shade the Area of the Circle Shade the Circumference of the Circle

Diameter – a line segment that passes through the center of the circle.

Radius – is a line segment that extends from the center of a circle to

any point on the circle.

To find the Area of a circle follow the following steps:

1) Write d =_____, r =_______

2) Write formula:

3) Substitute for r.

4) See how the answer should be shown. (Rounding or in terms of π)

Examples

a) r = 5 d = ______ b) r = 9 d = _______ c) r = ______ d = 8

d) r = _____ d = 12 e) r = 50 d = _______ f) r = 1 d = ______

g) r = 3 r2 = _____ h) r = 5 r2 = _______ i) r = 1 r2 = _____

Find the Area:

1)

Write r = ______

d = ______

Formula:

Substitute:

Solve: Answer in terms of π ________

Round answer to the nearest tenth _____

Find the area in terms of pi. Find the area and round to the nearest tenth.

2) r = ____ d = _____ 4) r = ____ d = _____

Write formula

3) r = ____ d = _____ 5) r = ____ d = _____

Given the Area, find the radius and diameter.

6) A = 49[pic] 7) A = 81[pic] 8) A = 16[pic] 9) A = 25[pic]

r = ______ r = ______ r = ______ r = ______

d = ______ d = ______ d = ______ d = ______

10) What is the radius and diameter of a circle with an Area equal to 113.04 sq. m? ________________

Find the Area of the following semicircles. (Round to nearest Tenth.)

11) A = ______ 12) A = ________

Diameter is 20 m Radius is 8.2 ft

Try These:

Find the Area of the following circles in terms of pi and to the nearest tenths place.

1) r = ____ d = _____ 2) r = ____ d = ______

3) 4) r = ____ d = ____

r = ____ d = _____

Given the Area, find the radius and diameter.

5) A = 121[pic] 6) A = 9[pic] 7) A = 225[pic] 8) A = 4[pic]

r = ______ r = ______ r = ______ r = ______

d = ______ d = ______ d = ______ d = ______

9)The area of a circle is 154 sq. m. What is the radius? ________________

What is the diameter? ______________

Lesson 3 - Homework

Find the Area of the following circles. Round your answer to the nearest tenth.

1) r = ____ d = _____ 2) r = ___ d =_____

A = A =

3) r = _____ d = ______ 4) r = ____ d =______

A = A =

Given the Area, find the radius and diameter.

5) A = 16Ï€ 6) A = 144Ï€

7)How much icing is needed to cover a Cake that has a diameter of 16 inches? (Leave in terms of π)

8) Find the area of the following: (careful it is a half circle) 9) Find the area of the circle below:

Round your answer to the nearest foot. Leave answer in terms of pi.

[pic]

Lesson 4

Finding Circumference of a Circle

To find the Circumference of a circle follow the following steps:

1) Write r =_____ d =_______

2) Write formula:

3) Substitute for d.

4) See how the answer should be shown. (Rounding or terms of π)

Examples:

Finding the Circumference

1)

Write r = ______

d = ______

Formula:

Substitute:

Solve:

Answer in terms of π ________

Round answer to the nearest tenth________

Find the circumference: In terms of π.

2) r = ____ d = _____ 3) r = ____ d = _____

Round to the nearest tenth.

4) r = ____ d = _____ 5) r = ____ d = _____

Find the Circumference of the following semicircles. (Round to nearest Tenth.)

6) C = ______ 7) C = ________

Diameter is 20 m Radius is 8.2 ft

Given the circumference, find the radius and diameter:

8) C = 4[pic] 9) C = 20[pic] 10) C = 50[pic] 11) C = 100[pic]

r = ______ r = ______ r = ______ r = ______

d = ______ d = ______ d = ______ d = ______

12) C = 81.7m 13) C = 94.2m 14) C = 18.8 ft 15) C = 188.5 ft

r = ______ r = ______ r = ______ r = ______

d = ______ d = ______ d = ______ d = ______

Try These:

Find the Circumference of the following circles in terms of pi and to the nearest tenths place.

1) r = ____ d = _____ 2) r = ____ d = ______

3) 4) r = ____ d = ____

r = ____ d = _____

Given the circumference, find the radius and diameter:

5) C = 80[pic] 6) C = 25[pic] 7) C = 36[pic] 8) C = 62[pic]

r = ______ r = ______ r = ______ r = ______

d = ______ d = ______ d = ______ d = ______

9) C = 50.3m 10) 150.8 ft 11) C = 12.6m 12) C = 100.5 ft

r = ______ r = ______ r = ______ r = ______

d = ______ d = ______ d = ______ d = ______

13) Chef Pierre uses vegetables grown in his new circular garden. He knows that the area of his garden is 15 square meters. He wants to build a path through the middle of the circular garden. What will be the approximate length of the new path?

New path design

A) 1.2m B) 2.2m C) 4.4m D) 7.2m

Lesson 4 - Homework

Find the Circumference of the following circles. Round your answer to the nearest tenth.

1) r = ____ d = _____ 2) r = ___ d =_____

C = C =

3) r = _____ d = ______ 4) r = ____ d =______

C = C =

5) How much fencing is needed for a garden that has a diameter of 10 ft? (Round to nearest tenth)

7) Joan determined the area of the circle below to be 400 𝝅 cm2 but Melinda says the area is 100 𝝅 cm2.

Who is correct? Why?

[pic]

Review:

8) Find the missing angle 9) Find the area of these two similar rectangles

9m 6m

12m x

Lesson 5

Area vs. Circumference

Sometimes you will be given the Area and be asked to find the Circumference.

Remember:

Steps:

1) Using the Area formula, plug in the given Area for A

2) Find the Radius by solving for r

3) Find the Diameter and use the Circumference formula to find the Circumference.

Examples

Find the Circumference of each in terms of[pic].

1) A = 25[pic] 2) A = 4[pic] 3) A = 121[pic]

Find the Circumference. Round to the nearest hundredth.

4) A = 153.938 m[pic] 5) A = 254.469 cm[pic] 6) A = 28.2743 ft[pic]

Sometimes you will be given the Circumference and be asked to find the Area.

Remember:

Steps:

1) Using the Circumference formula, plug in the given Circumference for C

2) Find the Diameter by solving for d

3) Find the Radius and use the Area formula to find the Area.

Find the Area of each in terms of[pic].

7) C = 10[pic] 8) C = 44[pic] 9) C = 8[pic]

Find the Area. Round to the nearest hundredth.

10) C = 37.6991 m 11) C = 62.8318 cm 12) C = 43.9822 ft

Try These

1) Hardy’s Pizzeria is having a sale on medium and large pizzas. Medium pizzas are 10 inches in

diameter and cost $7.99. Large pizzas have an area of 254 in[pic] and cost $14.99. Which size pizza

is the better deal? Explain.

______________________________________________________________________________________________________________________________________________________________________

2) If the length of the radius of a circle is doubled, how does that affect the circumference and area?

Explain.

______________________________________________________________________________________________________________________________________________________________________

3) Every year in September, Sue covers her circular pool. Her pool has a diameter of 25 feet. Find

how much covering she will need.

4) At a local park, Sara can choose between two circular paths to walk. One path has a diameter of 120

yards, and the other has a radius of 45 yards. How much further can Sara walk on the longer path

than the shorter path if she walks the path once?

5) Lana is putting lace trim around the border of a circular tablecloth. The tablecloth has a diameter of

1.2 meters. To the nearest meter, what is the least amount of lace she needs?

A. 3m B. 4m C. 7m D. 8m

6) The circle below has a diameter of 12 cm. Calculate the area of the shaded region.

[pic]

Lesson 5 - Homework

1) Given: A = 36[pic] 2) Given: C = 30[pic]

Find the Circumference in terms of [pic] Find the Area in terms of [pic]

3) Given: A = 452.3893m[pic] 4) Given: C = 50.2654cm[pic]

Find the Circumference round to nearest tenth. Find the Area rounded to nearest tenth.

5) A circular swimming pool has a radius of 15 feet. The family that owns the pool wants to put up a

circular fence that is 5 feet away from the pool at all points.

a) Find the radius of the fenced in area.

b) Find the amount of fencing needed.

6) What is the radius of a circle when the circumference is 16[pic] cm?

7) A circular rose garden needs new sod. The diameter of the garden is 18 feet. How much sod is

needed to cover the rose garden?

8) The front wheel of a high-wheel bicycle from the late 1800s was larger than the rear wheel to

increase the bicycle’s overall speed. The front wheel measured in height up to 60 in. Find the

circumference and area of the front wheel of the high-wheel bicycle.

9) Use the [pic] key on the calculator to find the area of a circle whose radius is 5.6m. Which is the better

estimate? 98m[pic] or 99m[pic]? Explain.

______________________________________________________________________________________________________________________________________________________________________

Name: ___________________________________________ Date: _________________

7ACC Unit 11 2D Figures Review

1) What is the best name of this quadrilateral?

_________________ __________________ __________________

Find the Area

2) 3) 4)

6m 8m 5.5m

9m 11m 4.2m

5) 7cm 6) 10m

5cm 8m

9cm

Find the area of the irregular figure.

7) 8m

5m

2m

8) Which figure has the least area?

A. Square with a side length of 11 cm

B. Parallelogram with a base of 8cm and height of 11cm

C. Triangle with a base of 18cm and a height of 4cm

D. Rectangle with a width of 5cm and a length of 18cm

The following figures are similar. Find the missing side.

40in

9) 10) 11)

12m 6m 18cm 12cm 160in 30in

20m x 6cm x

x

12) A man is 5 ft. tall and his shadow is 3 ft. long. A nearby tree has a shadow 6 ft. long. How

tall is the tree?

13) Jenny casts a shadow 4 meters long at the same time a tree casts a shadow 26 meters long.

Jenny is 22 meters tall. How tall is tree?

Find the perimeter of the following similar figure. Find the area of the following similar figure.

14) 15)

20m 20m 15m 5m

10m 10m

30m x

5m x

16) Kelly has two rectangular photo prints that are similar. The length of the smaller

print is 4 inches and the width is 5 inches. The length of the larger print is 20 inches.

a) Find the width of the larger print.

b) Find the perimeter of the smaller print.

c) Find the area of the larger print.

Find the circumference and area in terms of pi.

17) C = ____ A = _____ 18) C = ____ A = _____

Find the circumference and area to the nearest tenth.

19) C = ____ A = _____ 20) . C = ____ A = _____

21) How much covering is needed to cover a Cake that has a diameter of 12 inches? (Leave in

terms of π)

Find the circumference of each in terms of [pic]. Find the circumference to the nearest hundredth.

22) A = 36[pic] 23) A = 9[pic] 24) A = 452.3893 m[pic] 25) A = 314.1592 cm[pic]

Find the area of each in terms of [pic]. Find the area rounded to the nearest hundredth.

26) C = 12[pic] 27) C = 8[pic] 28) C = 62.8318 m 29) C = 113.0973 cm

30) The window that is in the shape of a semicircle has a diameter of 12 inches. Find the area of

the window. Round to the nearest tenth.

31) Kara wants to put fencing around her pool. Her pool has a diameter of 14 feet. Find

how much fencing she will need.

32) What is the radius of a circle when the circumference is 25[pic] cm?

-----------------------

10

4

8

16

20

12

4

20

9

7

9

9

15

20

11

4

10

2.5

1.2

10

50

8

5

90

12

90

diameter

radius

[pic]

4m

24m

3m

10m

9m[pic]m

8m

3m

10m

50m

18m

8m 8888m

6m

22m

[pic]

12m

13m

7m

24m

4m[pic]m

8m

3m

5m

50m

10m

18m

8m 8888m

6m

22m

100[pic]

135[pic]

70[pic]

x

[pic]

[pic]

5m

12m

8m[pic]m

4.5m

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download