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By Mrs. Czajkowski

By Mrs. Czajkowski. A Polygons 100 200 300 400 500 600 700 800 900 1000 B Perimeter 100 200 300 400 500 600 700 800 900 1000 C Area 100 200 300 400 500

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Page 1: By Mrs. Czajkowski. A Polygons 100 200 300 400 500 600 700 800 900 1000 B Perimeter 100 200 300 400 500 600 700 800 900 1000 C Area 100 200 300 400 500

By

Mrs. Czajkowski

Page 2: By Mrs. Czajkowski. A Polygons 100 200 300 400 500 600 700 800 900 1000 B Perimeter 100 200 300 400 500 600 700 800 900 1000 C Area 100 200 300 400 500

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Volume

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Page 3: By Mrs. Czajkowski. A Polygons 100 200 300 400 500 600 700 800 900 1000 B Perimeter 100 200 300 400 500 600 700 800 900 1000 C Area 100 200 300 400 500

A100

Answer: A pentagon is a five sided polygon.

Question: What is the name of a

five sided polygon?

Page 4: By Mrs. Czajkowski. A Polygons 100 200 300 400 500 600 700 800 900 1000 B Perimeter 100 200 300 400 500 600 700 800 900 1000 C Area 100 200 300 400 500

A200

Answer: An octagon has eight sides.

Question: How many sides

does an octagon have?

Page 5: By Mrs. Czajkowski. A Polygons 100 200 300 400 500 600 700 800 900 1000 B Perimeter 100 200 300 400 500 600 700 800 900 1000 C Area 100 200 300 400 500

A300

Answer: Three sides are needed

to make a polygon.

(That polygon is called a triangle!)

Question: What is the fewest number of

sides needed to make a polygon?

Page 6: By Mrs. Czajkowski. A Polygons 100 200 300 400 500 600 700 800 900 1000 B Perimeter 100 200 300 400 500 600 700 800 900 1000 C Area 100 200 300 400 500

A400

Answer: A trapezoid is a quadrilateral

that has two parallel bases.

Question: What is a quadrilateral that

has two parallel bases called?

Page 7: By Mrs. Czajkowski. A Polygons 100 200 300 400 500 600 700 800 900 1000 B Perimeter 100 200 300 400 500 600 700 800 900 1000 C Area 100 200 300 400 500

A500

Answer: A decagon has 10 sides

and it also has 10 angles.

Question: How many sides and how many

angles does an decagon have?

Page 8: By Mrs. Czajkowski. A Polygons 100 200 300 400 500 600 700 800 900 1000 B Perimeter 100 200 300 400 500 600 700 800 900 1000 C Area 100 200 300 400 500

A600

Answer: A quadrilateral can have no

more than two obtuse angles.

Question: What is the greatest number of

obtuse angles that a quadrilateral can have?

Page 9: By Mrs. Czajkowski. A Polygons 100 200 300 400 500 600 700 800 900 1000 B Perimeter 100 200 300 400 500 600 700 800 900 1000 C Area 100 200 300 400 500

A700

Answer: A rectangle is equiangular,

but not equilateral.

Question: Which type of quadrilateral is an

equiangular quadrilateral, but is

not an equilateral quadrilateral?

Page 10: By Mrs. Czajkowski. A Polygons 100 200 300 400 500 600 700 800 900 1000 B Perimeter 100 200 300 400 500 600 700 800 900 1000 C Area 100 200 300 400 500

A800

Answer:A regular polygon is a polygon that

has all congruent sides and all

congruent angles.

Question:You know what a polygon is!

Now, define regular polygon.

Page 11: By Mrs. Czajkowski. A Polygons 100 200 300 400 500 600 700 800 900 1000 B Perimeter 100 200 300 400 500 600 700 800 900 1000 C Area 100 200 300 400 500

A900

Answer: A rhombus has all sides congruent,

but its angles are not.

Question: Which type of quadrilateral is

equilateral but not equiangular?

Page 12: By Mrs. Czajkowski. A Polygons 100 200 300 400 500 600 700 800 900 1000 B Perimeter 100 200 300 400 500 600 700 800 900 1000 C Area 100 200 300 400 500

A1000

Answer: A square and a rhombus are the

quadrilaterals that have four

congruent sides.

Question: Name all the quadrilaterals

that have four congruent sides.

Page 13: By Mrs. Czajkowski. A Polygons 100 200 300 400 500 600 700 800 900 1000 B Perimeter 100 200 300 400 500 600 700 800 900 1000 C Area 100 200 300 400 500

B100

Answer:The perimeter of a triangle

that has sides measuring 4 cm, 5cm,

and 8 cm is 17 centimeters.

Question: What is the perimeter of a triangle

that has sides measuring 4 cm, 5cm,

and 8 cm ?

Page 14: By Mrs. Czajkowski. A Polygons 100 200 300 400 500 600 700 800 900 1000 B Perimeter 100 200 300 400 500 600 700 800 900 1000 C Area 100 200 300 400 500

B200

Answer: The perimeter of a rectangle that is

8 centimeters long and 3 centimeters

wide is 22 centimeters.

Question: What is the perimeter of a

rectangle that is 8 centimeters

long and 3 centimeters wide?

Page 15: By Mrs. Czajkowski. A Polygons 100 200 300 400 500 600 700 800 900 1000 B Perimeter 100 200 300 400 500 600 700 800 900 1000 C Area 100 200 300 400 500

B300

Answer: A regular octagon has eight

congruent sides. Its perimeter

would be 64 centimeters.

Question: What is the perimeter of a

regular octagon that has a side that

measures 8 centimeters?

Page 16: By Mrs. Czajkowski. A Polygons 100 200 300 400 500 600 700 800 900 1000 B Perimeter 100 200 300 400 500 600 700 800 900 1000 C Area 100 200 300 400 500

B400

Answer: Calculate the square root of the

area to find the length of a side

of the square. Multiply that

length by four to find the perimeter!

Question: Describe a method of finding the

perimeter of a square if you know

the area of the same square.

Page 17: By Mrs. Czajkowski. A Polygons 100 200 300 400 500 600 700 800 900 1000 B Perimeter 100 200 300 400 500 600 700 800 900 1000 C Area 100 200 300 400 500

B500

Answer: The length of the rectangle is 24

feet and the width is 12 feet.

(Check: 24 + 12 + 24 + 12 = 72)

Question: If the length of a rectangle

measures twice the width, and the

perimeter is 72 feet, find the

dimensions of the rectangle.

Page 18: By Mrs. Czajkowski. A Polygons 100 200 300 400 500 600 700 800 900 1000 B Perimeter 100 200 300 400 500 600 700 800 900 1000 C Area 100 200 300 400 500

B600

Answer: Each side of the triangle

measures 9 centimeters.

Question: The perimeter of an equilateral

triangle is 27 centimeters. Find the

measure of each of its sides.

Page 19: By Mrs. Czajkowski. A Polygons 100 200 300 400 500 600 700 800 900 1000 B Perimeter 100 200 300 400 500 600 700 800 900 1000 C Area 100 200 300 400 500

B700

Answer: The perimeter of the triangle is

6 + 12 + 12 or 30 inches.

Question: The base of an isosceles triangle

measures 6 inches. If the measure

of each of the congruent sides is

twice the measure of the base, find

the perimeter of the triangle.

Page 20: By Mrs. Czajkowski. A Polygons 100 200 300 400 500 600 700 800 900 1000 B Perimeter 100 200 300 400 500 600 700 800 900 1000 C Area 100 200 300 400 500

B800

Answer: The perimeter of the square

is 4 times 6 or 24 inches.

Question: The area of a square is

36 square inches. Find the

perimeter of the square.

Page 21: By Mrs. Czajkowski. A Polygons 100 200 300 400 500 600 700 800 900 1000 B Perimeter 100 200 300 400 500 600 700 800 900 1000 C Area 100 200 300 400 500

B900

Answer: The perimeter is

3 + 4 + 3 + 4 or 14 yards.

Question: A rectangle measures 9 feet

by 12 feet. How many yards

are in the perimeter of the

rectangle?

Page 22: By Mrs. Czajkowski. A Polygons 100 200 300 400 500 600 700 800 900 1000 B Perimeter 100 200 300 400 500 600 700 800 900 1000 C Area 100 200 300 400 500

B1000

Answer: The perimeter of the

trapezoid is

8+ 8 + 10 + 15 or 41 inches.

Question: An isoceles trapezoid has bases that

measure 10 inches and 15 inches. A

side of the trapezoid measures 8

inches. Find the perimeter.

Page 23: By Mrs. Czajkowski. A Polygons 100 200 300 400 500 600 700 800 900 1000 B Perimeter 100 200 300 400 500 600 700 800 900 1000 C Area 100 200 300 400 500

C100

Answer: The area is 32 square centimeters.

Question: Calculate the area of an

isosceles right triangle that has

legs measuring 8 centimeters.

Page 24: By Mrs. Czajkowski. A Polygons 100 200 300 400 500 600 700 800 900 1000 B Perimeter 100 200 300 400 500 600 700 800 900 1000 C Area 100 200 300 400 500

C200

Answer: The altitude measures 4 yards.

Question: The area of a trapezoid is 24 square

yards. The measures of the bases

are 3 yards and 9 yards.

Find the measure of the altitude.

Page 25: By Mrs. Czajkowski. A Polygons 100 200 300 400 500 600 700 800 900 1000 B Perimeter 100 200 300 400 500 600 700 800 900 1000 C Area 100 200 300 400 500

C300

Answer: The area is 90 times 90 or

8100 square feet.

Question: A baseball diamond is a square

measuring 90 feet on each side.

What is the area of the infield

(inside the diamond)?

Page 26: By Mrs. Czajkowski. A Polygons 100 200 300 400 500 600 700 800 900 1000 B Perimeter 100 200 300 400 500 600 700 800 900 1000 C Area 100 200 300 400 500

C400

Answer: 48 squares will fit into the rectangle.

Question: How many 1” by 1” squares will fit

into a rectangle that measures

4” by 12” ?

Page 27: By Mrs. Czajkowski. A Polygons 100 200 300 400 500 600 700 800 900 1000 B Perimeter 100 200 300 400 500 600 700 800 900 1000 C Area 100 200 300 400 500

C500

Answer: (Notice that one of the bases is

measured in meters!!!) The area of the

trapezoid is 780 square centimeters.

Question: What is the area of a trapezoid that

has a height of 12 centimeters and

bases of 2 meters and 30 centimeters?

Page 28: By Mrs. Czajkowski. A Polygons 100 200 300 400 500 600 700 800 900 1000 B Perimeter 100 200 300 400 500 600 700 800 900 1000 C Area 100 200 300 400 500

C600

Answer: The kitchen floor is 15 square

yards. It would cost $105 to

cover the kitchen floor.

Question: Linoleum costs $7 a square yard.

Calculate the cost to cover a

9 foot by 15 foot kitchen floor.

Page 29: By Mrs. Czajkowski. A Polygons 100 200 300 400 500 600 700 800 900 1000 B Perimeter 100 200 300 400 500 600 700 800 900 1000 C Area 100 200 300 400 500

C700

Answer: The other leg of the triangle

measures 12 inches.

Question: The area of a right triangle is

84 square inches. If one leg

measures 14 inches, find the

measure of the other leg.

Page 30: By Mrs. Czajkowski. A Polygons 100 200 300 400 500 600 700 800 900 1000 B Perimeter 100 200 300 400 500 600 700 800 900 1000 C Area 100 200 300 400 500

C800

Answer: (The sides of the smaller square

measure 7 meters.)

The sides of the larger

square must measure

14 meters!

Question: The area of a small square is 49

square meters. A larger square has

sides that are twice as long. What

is the measure of one side of the

larger square?

Page 31: By Mrs. Czajkowski. A Polygons 100 200 300 400 500 600 700 800 900 1000 B Perimeter 100 200 300 400 500 600 700 800 900 1000 C Area 100 200 300 400 500

C900

Answer: The area of the rectangle is

2 times 15 or 30 square inches.

Question: Find the area of a rectangle that

has a perimeter of 34 inches and

a base of 15 inches.

Page 32: By Mrs. Czajkowski. A Polygons 100 200 300 400 500 600 700 800 900 1000 B Perimeter 100 200 300 400 500 600 700 800 900 1000 C Area 100 200 300 400 500

C1000

Answer: The rectangle has an area

of 12 square yards.

Question: The dimensions of a rectangle

are 9 ft. by 12 ft. Find the

number of sq. yds. in the area

of the rectangle.

Page 33: By Mrs. Czajkowski. A Polygons 100 200 300 400 500 600 700 800 900 1000 B Perimeter 100 200 300 400 500 600 700 800 900 1000 C Area 100 200 300 400 500

D100

Answer: The volume of the cube

is 216 cubic centimeters.

Question: Find the volume of a cube that

measures 6 centimeters on a side.

Page 34: By Mrs. Czajkowski. A Polygons 100 200 300 400 500 600 700 800 900 1000 B Perimeter 100 200 300 400 500 600 700 800 900 1000 C Area 100 200 300 400 500

D200

Answer: The volume is 54 times 8

which equals 432 cubic inches.

Question: Find the volume of a rectangular

prism that has a base area of 54

square inches and a height of 8 inches.

Page 35: By Mrs. Czajkowski. A Polygons 100 200 300 400 500 600 700 800 900 1000 B Perimeter 100 200 300 400 500 600 700 800 900 1000 C Area 100 200 300 400 500

D300

Answer: The volume of the cylinder

is 235.5 cubic inches.

Question: Find the volume of a cylinder whose

base has a radius of 5 inches, and

whose height measures 3 inches.

(Use = 3.14)

Page 36: By Mrs. Czajkowski. A Polygons 100 200 300 400 500 600 700 800 900 1000 B Perimeter 100 200 300 400 500 600 700 800 900 1000 C Area 100 200 300 400 500

D400

Answer: The volume of the prism is

214.2 cubic centimeters.

Question: Find the volume of a rectangular

prism that has a lenth of 8.5 cm, a

width of 4.2 cm, and a height of 6 cm.

Page 37: By Mrs. Czajkowski. A Polygons 100 200 300 400 500 600 700 800 900 1000 B Perimeter 100 200 300 400 500 600 700 800 900 1000 C Area 100 200 300 400 500

D500

Answer: A cubic meter is equal to 1000

cubic centimeters. The liquid would

weigh 2000 grams or 2 kilograms.

Question: If one cubic centimeter of a

liquid weighs 2 grams, how much

does one cubic meter of the same

liquid weigh?

Page 38: By Mrs. Czajkowski. A Polygons 100 200 300 400 500 600 700 800 900 1000 B Perimeter 100 200 300 400 500 600 700 800 900 1000 C Area 100 200 300 400 500

D600

Answer: The volume is equal to 28 cubic inches.

Question: Find the volume of a pyramid that is

4 inches high, and has a rectangular base

that is 6 inches long and 3.5 inches wide.

Page 39: By Mrs. Czajkowski. A Polygons 100 200 300 400 500 600 700 800 900 1000 B Perimeter 100 200 300 400 500 600 700 800 900 1000 C Area 100 200 300 400 500

D700

Answer: Cheop’s pyramid had a volume of

2,592,100 cubic meters.

Question: The largest pyramid in the world was

built around 2500 B.C. by Khufu, or Cheops,

a king of ancient Egypt. The pyramid had a

square base, 230 meters on each side, and

a height of 147 meters. Find the volume of

Cheop’s pyramid.

Page 40: By Mrs. Czajkowski. A Polygons 100 200 300 400 500 600 700 800 900 1000 B Perimeter 100 200 300 400 500 600 700 800 900 1000 C Area 100 200 300 400 500

D800

Answer: The volume is equal to 4410.

Question: What is the exact volume of a

cylinder that has a 21 inch radius

and a height of 10 inches?

Page 41: By Mrs. Czajkowski. A Polygons 100 200 300 400 500 600 700 800 900 1000 B Perimeter 100 200 300 400 500 600 700 800 900 1000 C Area 100 200 300 400 500

D900

Answer: The volume is equal to 98.

Question: A cone has a base that is 14 inches

wide. The height of the cone is 6 inches.

Find the exact volume of the cone.

Page 42: By Mrs. Czajkowski. A Polygons 100 200 300 400 500 600 700 800 900 1000 B Perimeter 100 200 300 400 500 600 700 800 900 1000 C Area 100 200 300 400 500

D1000

Answer: The volume is equal to 36,000.

Question: Find the exact volume of a sphere

that has a radius of 30 cm.

3r