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Formulae for Geometry

Pythagorean Theorem: a² +b = c?

sin A=

opposite

hypotenuse

hypotenuse

opposite

Conversion factors:

1 yd = 3 ft = 36 inches

1 ft = 12 inches

1 mile = 5280 ft

adjacent

1 m = 100 cm = 1000 mm

1 km = 1000 m

adjacent

cos A=

hypotenuse

opposite

tan A =

adjacent

1 mile = 1.6 km

1 yd = 0.9 m

1 in = 2.54 cm

1 lb = 0.45 kg

A = area; b = base; C = circumference; h= height;

1 = length; r= radius; SA = surface area; V = volume

Circle: C = 27r; A=Tr?

Rectangle: P=2b +2h; A=bh

Triangle Area Formulas:

Trapezoid: A= +

2

A= -bh

1= -6

Heron’s Formula: A= Vs(s – a)(s – b)(s-c)

h

1

where s=-(a+b+c)

2

b.

Surface Area = the sum of the areas of each exterior surface of the 3-dimensional figure

4

Cylinder: V = ar’h; SA=2 r(r+h) Sphere: V =

ar?; SA= 47 r2

Solid with matching base and top (equal cross sections):

V =(area of base)* h

Cone Volume: V = Farh

Pyramid Volume: V =-(area of base) * h

2.

3

4

A gas station is 9 miles away. How far is the gas station in Kilometers? Use the following comes

km

Х

5

?

3

4

5

6

7

8

10

way. How far is the gas station in kilometers? Use the following conversion: 1 mile is 1.6 kilometers

Х

5

?

1

2

3

4

5

6

7

While studying abroad, Christine wants to make 5 batches of her mother’s enchilada

batch. The local market sells cheese by the gram. How many grams of cheese should

Use 1 oz=28 g and do not round any computations.

1 g

Х

5

?

10

F her mother’s enchilada recipe to feed her classmates. The recipe calls for 16 of cheese for each

grams of cheese should Christine buy?

Question 3 of 15 (5 points) | Question Attempt: 1 of 1

2

4

5

6

7

8

9

A flower bed is in the shape of a rectangle. It measures

5 yd long and 4 yd wide. Ravi wants to use mulch to

cover the flower bed. The mulch is sold by the square

foot. Use the facts to find the area of the flower bed in

square feet.

Conversion facts for length

1 foot (ft) 12 inches (in)

1 yard (yd) 3 feet (ft)

1 yard (yd) = 36 inches (in)

Х

s ?

5

6

7

A jogging track has a length of 0.35 miles (mi). How long is this in yards (yd)?

First fill in the blank on the left side of the equation using one of the ratios. Then write your answer on the right side of the ti

1 ft

Ratios:

12 in

1760 yd

1 mi

12 in

1 mi

1 ft

5280 Ft

1 mi

1760 yd

Yd

5280 ft

I mi

0.35 mi

1

X

Ú

Iya

Х

yd

8

8

9

10

11

12

13

14

is in the shape of a rectangle. Its length is 46 feet and its width is 35 feet. Suppose each can of wood

eed to cover the court?

011

1

2

3

4.

5

6

7

Boris is staining the wooden floor of a court. The court is in the shape of a rectangle. Its length is 46 feet and its

stain covers 115 square feet. How many cans will he need to cover the court?

cans

Х

Ś

?

5

7

8

10

11

A metal warehouse, whose dimensions are shown below, needs paint. The front and back of the warehouse each have 2 roll-

each. The side of the warehouse facing the parking lot has an entry door measuring 64 in by 81 in. The other side of the w

Use the given information to answer the questions. Each tab shows a different view of the warehouse.

(a) Assuming the roof and doors require no paint, what

is the area in square feet that needs paint? (Do not

round any intermediate computations and give your

answer as a whole number.)

Conversion facts for length

1 foot (ft) = 12 inches (in)

1 yard (yd) = 3 feet (A)

1 yard (yd) = 36 inches (in)

=

[

2

ft

Front-right view

Back-left vie

(b) The paint to be used is sold in cans. Each can

contains enough paint to cover 450 ft”. Assume

there is no paint yet and partial cans cannot be

bought. How many cans will need to be bought in

order to paint the warehouse?

Ic

cans

11

12

13

14

s are shown below, needs paint. The front and back of the warehouse each have 2 rollup doors measuring 23 ft by 29 ft

g the parking lot has an entry door measuring 64 in by 81 in. The other side of the warehouse has no window or door.

e questions. Each tab shows a different view of the warehouse.

equire no paint, what

needs paint? (Do not

cations and give your

Conversion facts for length

BREE

1 foot (ft) = 12 inches (in)

1 yard (yd) 3 feet (ft)

1 yard (yd) = 36 inches (in)

Front-right view

Back-eft view

s. Each can

O ft?. Assume

ns cannot be

o be bought in

35 ft

(a) Assuming the roof and doors require no paint, what

is the area in square feet that needs paint? (Do not

round any intermediate computations and give your

answer as a whole number.)

Conversion facts for length

1 foot (ft) = 12 inches (in)

1 yard (yd) = 3 feet (ft)

1 yard (yd) 36 inches (in)

2

ft

Front-right view

Back-left view

.

(b) The paint to be used is sold in cans. Each can

contains enough paint to cover 450 ft. Assume

there is no paint yet and partial cans cannot be

bought. How many cans will need to be bought in

order to paint the warehouse?

1

cans

35 ft

c) What is the total cost of the paint needed for the

warehouse if each can costs $41.50?

s[]

44 ft

50 ft

Х

$

a

?

I yard (yd) 3 feet (ft)

1 yard (yd) = 36 inches (in)

Front-right view

Back left view

3

ed is sold in cans. Each can

2

int to cover 450 ft. Assume

t and partial cans cannot be

cans will need to be bought in

arehouse?

35 ft

of the paint needed for the

n costs $41.50?

44 ft

50 ft

3

(a) Find the exact circumference and area of the courtyard. Write your answers in terms of t. Make

sure to use the correct units in your answers.

8

UU

Exact circumference: 1

Exact area:

O

m

x

Х

(b) Approximate the circumference and area of the courtyard. To do the approximations, use the it

button on the ALEKS calculator and round your answers to the nearest hundredth. Make sure to

use the correct units in your answers.

Approximate circumference:

Approximate area:

(c) A chain will surround the courtyard.

Which measure would be used in finding the amount of chain needed?

Circumference

Area

(d) The courtyard will be paved.

Which measure would be used in finding the amount of pavement needed?

Circumference

Area

8

9

10

11

The diameter of a circular courtyard is 68 m.

Answer the parts below. If necessary, refer to the list of geometry formulas.

68 m

(a) Find the exact circumference and area of the courtyard. Write your answers in terms of t. Make

sure to use the correct units in your answers.

B

금

Exact circumference: 1

Exact area:

.

m

Х

(b) Approximate the circumference and area of the courtyard. To do the approximations, use the t

button on the ALEKS calculator and round your answers to the nearest hundredth. Make sure to

use the correct units in your answers.

Approximate circumference: |

Approximate area:

(C) A chain will surround the courtyard.

Which measure would be used in finding the amount of chain needed?

1

2

5

A company makes concrete bricks shaped like rectangular prisms. Each brick is 15 inches long, 10 inches wie

concrete, how many bricks did they make?

bricks

X

5

?

9

10

12

13

ped like rectangular prisms. Each brick is 15 inches long, 10 inches wide, and 5 inches tall. If they used 15,000 in of

ke?

?

1

2

3

4

5

6

7

8

10

A rose garden is formed by joining a rectangle and a semicircle, as shown below. The rectangle is 31 ft long and 24

Find the area of the garden. Do not round any intermediate steps. Round your final answer to the nearest hundred

If necessary, refer to the list of geometry formulas.

24 ft

31 ft

10

11

12

13

angle and a semicircle, as shown below. The rectangle is 31 ft long and 24 ft wide.

any intermediate steps. Round your final answer to the nearest hundredth and be sure to include the correct unit.

formulas.

DO

금

ft

ft2

ft

X 5

?

om the top of the building to the tip of the shadow is 33 m. Find the height of the bundingu

I

m

x 5

?

2

3

4

5

6

7

8

The length of a shadow of a building is 29 m. The distance from the top of the building to the ti

necessary, round your answer to the nearest tenth.

m

33

In01

29

Stone 103

2

3

5

7

A pole that is 2.5 m tall casts a shadow that is 1.16 m long. At the same time, a nearby building casts a shado

Round your answer to the nearest meter.

0

m

Х

5

?

5

6

7

8

10

on

12

is 1.16 m long. At the same time, a nearby building casts a shadow that is 50.25 mg, Misheng

?

9

A right triangle has side lengths 5, 12, and 13 as shown below.

Use these lengths to find cos A, tan A, and sin A.

cos A =

B

o

13

Х

1

5

tan A =

А

12

C

sin A =

1

2

3

4

5

6

7

8

10

A ladder leans against the side of a house. The angle of elevation of the ladder is 61°, and the top of the ladder is 15 ft at

from the bottom of the ladder to the side of the house. Round your answer to the nearest tenth.

Ut

ft

X

15

61°

?

14

evation of the ladder is 61°, and the top of the ladder is 15 ft above the ground. Find the distance

und your answer to the nearest tenth.

ft

Х

$

?

2

3

4

5

6

8.

9

10

A company rents water tanks shaped like cylinders. Each tank has a radius of 6 feet and a height of 4 feet. The cost is $2

to rent one water tank?

If necessary, refer to the list of geometry formulas.

For your calculations, do not round any intermediate steps, and use the it button on the ALEKS calculator. Round you

s]

?

10

11

13

nders. Each tank has a radius of 6 feet and a height of 4 feet. The cost is $2 per cubic foot. How much does it cost.

ulas.

Siate steps, and use the button on the ALEKS calculator. Round your answer to the nearest cent.

?

Purchase answer to see full

attachment

Explanation & Answer:

10 questions

Tags:

geometry

Pythagorean Theorem

triangle area

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