Geometry – Group A Section 7 – 1 Understanding Perimeter ...

[Pages:13]Geometry ? Group A Section 7 ? 1 Understanding Perimeter and Area

(Green Book Section 9-1)

Find the perimeter of each figure.

1.

11 ft

2. 6 cm

Find the perimeter of each rectangle with the given base and height.

3. 21 in., 7 in.

4. 24 m, 36 m

2 cm

The figures below are drawn on centimeter graph paper. Find the area of the shaded portion.

5.

6.

Graph each rectangle ABCD and find its area.

7. A(0, 0), B (0, 4),C (5, 4), D (5, 0)

y

8. A(-3, 2), B (-2, 2),C (-2, -2), D (-3, -2)

y

x

x

9. The perimeter of a rectangle is 40 cm and the base is 12 cm. What is the area? 10. A square and a rectangle have equal areas. The rectangle is 64 cm by 81 cm. What is the

perimeter of the square?

Find the area of each rectangle with the given base and height. 11. 4ft 6 in., 4 in.

12. Building Safe Stairs: Since falls are a major cause of injury, is makes sense to be concerned about the safety of stairs. According to John Templer, the world's foremost authority of stairs, steps with a 7-in. riser and an 11-in. tread form the safest possible stairs. Prior to his investigations, Francois Blondel's formula dated 1675, had recommended that stair measurements conform to the formula 2(riser) + tread=25.5 in.

You use John Templer's dimensions to build a stairway with six steps. You want

to carpet the stairs with a 3-foot wide runner from the bottom of the first

riser to the top of the sixth riser. a. Find the area of the runner.

riser

b. Since a roll of carpet is 12 ft across, a rectangle of carpet that

measures 3 ft by 12 ft is cut from the roll to make the runner.

How many square feet of the material will be wasted. c. The carpet costs $17.95/yd2. You must pay for the entire piece

that is cut. Find the cost of the carpet.

d. Binding for the edge of the runner costs $1.75/yd. How

much will the binding cost if the two long edges of

the runner are bound?

tread

Tell whether you need to know area or perimeter in order to determine how much of each item to buy.

13. edging for a garden

14. wallpaper for a bedroom

15. The Art Club is tiling an 8 ft-by-16 ft wall at the entrance to the school. They are creating a design by using different colors of 4 in.-by-4 in. tiles. How many tiles do the students need?

16. You want to make a 900-ft2 rectangular garden to grow corn. In order to keep raccoons out of your corn, you must fence the garden. You want to use the minimum amount of fencing so that your costs will be as low as possible. List at least three possible dimensions for the rectangular garden. Find the perimeter of each rectangle.

Find the area of the shaded portion of each figure. All angles in the figures are right angles.

17.

20 m

18. 2 yd

4 yd

19.

20.

4 in.

1 yd

18 m 4 yd

5 m

10 m 5 m

6 cm 3 yd 3 yd

8 in.

4 in.

12 in.

6 cm

Geometry ? Group A Section 7 ? 2 Measuring in the Plane

(Green Book Section 9-1y)

Find the area of each figure.

F

1. DJK

2. ADKF

A

J

K

BC D

x

3. The area of a parallelogram is 24 in.2 and the height is 6 in. Find the length of the base.

Find the area of each shaded region.

4.

5.

6.

15 cm 12 cm 3 ft

20 cm

2 ft

2 ft

Find the value of h is each parallelogram. 7.

h

14

8

10

8. 0.3

3.5 cm

5.8 cm

4 cm

0.5 h

0.4

9. Taisha's Bakery has a plan for a 50 ft-by-31 ft parking lot. The four parking spaces are congruent parallelograms, the driving area is a rectangle, and the two unpaved areas for flowers are congruent triangles. a. Explain two different ways to find the area of the region that must be paved. b. Verify your answer to part (a) by using each method to find the area.

50 ft 15 ft 31 ft

10 ft

Find the area of each figure.

10.

11.

12.

13. Ann drew these three figures on a grid. A fly landed at random at a point on the grid. a. Is the fly more likely to have landed on one of the figures or on the blank grid? Explain. b. Suppose you know the fly landed on one of the figures. Is the fly more likely to have landed on one figure than another? Explain.

Find the area of each figure.

14.

25 ft

15. 15 cm

16.

200 m

25 ft 25 ft

21 cm

20 cm

120 m 40 m

60 m

The vertices of a polygon are given. Graph each polygon and find its area.

17. A(3,9), B (8,9),C (2, -3), D (-3, -3)

18. E (1,1), F (4,5),G (11,5), H (8,1)

y

y

x

19. M (-2, -5), L (1, -5), N (2, -2)

y x

x

20. R (1, 2), S (1, 6),T (4,1)

y

x

Geometry ? Group A Section 7 ? 3 The Pythagorean Theorem and its Converse

(Green Book Section 5-7)

Find the value of x. Leave your answer in simplest radical form.

1.

2.

x 10

x

6

3. 3

2

x

16

3

x

4. A 15-ft tall ladder is leaning against a building. The base of the ladder is 5 ft from the building. To the nearest foot, how high up the building does the ladder reach?

5. A brick walkway forms the diagonal of a square playground. The walkway is 24 m long. To the nearest tenth of a meter, how long is a side of the playground?

The lengths of the sides of a triangle are given. Classify each triangle as acute, right, or obtuse.

6. 15, 8, 21

7. 30, 34, 16

8. 11, 12, 15

9. 12, 16, 20

10. 2, 3, 3

11. 7, 11, 4

Use the triangle at the right. Find the length to the nearest tenth.

12. a = 3,b = 7, c =

13. a = 1.2,b = , c = 3.5

14. a = 8,b = 8, c =

15. a = ,b = 9, c = 18

Find the area of each figure. Leave your answer in simplest radical form.

16.

17.

6 m

10 ft 8 ft

17 ft

3 m

Find a third number so that the three numbers form a Pythagorean Triple.

18. 9, 41

19. 14, 48

20. 12, 37

Geometry ? Group A Section 7 ? 4 Special Right Triangles

(Green Book Section 5-8)

Find the value of each variable. Leave your answers in simplest radical form.

1.

2.

3.

y 8

45? x

y

15 2

y

45?

x

30? 23

4. 23 60?

y x

5. y x

45? 2

6. A conveyor belt carries bales of hay from the ground to the loft of a barn 27.5 ft above the ground. The belt makes a 30? angle with the ground. How far does the hay travel on the conveyor belt?

b. The conveyor belt moves at 100ft/min. How long does it take for a bale of hay to go from the ground to the barn loft?

Find the value of each variable. Leave your answers in simplest radical form.

7.

8.

9.

y

60

45?

40 x

30? y

43

60? c

b a

45? d

10. a

30? c

b 10 60? d

11. 23

6 60? a

b

12. Sandra drew this triangle. Rika said that the lengths couldn't be correct. With which student do you agree? Explain.

5

30? 10

53 60?

13. Which of the following cannot be the lengths of sides of a 30? - 60? - 90? triangle?

A. 1 ,1, 3 22

B. 3, 2 3, 3

C. 1, 1 , 3 2

D. 2 2, 2, 6

E. 2, 4, 2 3

Find the area of each figure. Round answers to the nearest tenth

14.

15.

16.

8 3 cm 24 ft

45? 14 2 m

60?

60?

17. The blades of a helicopter meet at right angles and are all the same length. The distance between the tips of the two consecutive blades is 36 ft. How long is each blade? Round your answer to the nearest tenth.

18. The hypotenuse of a 30? - 60? - 90? triangle is 12 ft long. Write a real life problem that you can solve using this triangle. Show your solution.

19. A rhombus has a 60? angle and sides 5 cm long. What is its area? Round you answers to the nearest tenth.

Geometry ? Group A Section 7 ? 5 Areas of Trapezoids

(Green Book Section 9-1) Find the area of each trapezoid. 1.

21 in.

16 in.

38 in.

3. 5 ft 3 ft

6 ft

2. 24.3 cm

8.5 cm 9.7 cm

4. 10 m

6 m 8 m

5. Approximate the area of Nevada by finding the area of the trapezoid shown.

6. The area of a trapezoid is 80 ft2. Its bases have lengths 26 ft and 14 ft. Find its height.

212 mi

315 mi

7. (a). A trapezoid has two right angles, bases of lengths 12 m and 18 m, and a height of 8 m. Sketch the trapezoid.

(b). What is the perimeter?

(c). What is the area?

480 mi

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