Skill: Perimeter/Area/Volume

Standard: 5.8.a ~ The student will find perimeter, area, and volume in

standard units of measure

5.8.b ~ The student will differentiate among perimeter, area, and

volume and identify whether the application of the concept of

perimeter, area, or volume is appropriate for a given situation;

Vocabulary:

Perimeter – The distance around the outside of a polygon

Area – The amount of space or “squares” inside a shape

Volume – The amount of space or “cubes” inside a three-

dimensional object

Perimeter You can calculate the perimeter by adding the lengths of the sides together.

Triangles

P = 4 + 4 + 6

P = 14 cm

Parallelograms

*One thing you need to know about parallelograms is that opposite sides are congruent.

1st, you need to write in the opposite sides

P = 5 + 5 + 2 + 2

P = 14 in

4 cm 4 cm

6 cm

5 in

2 in. 2 in

5 in

Units used to describe perimeter:

(Regular Units)

Customary: Metric:

Inches (in) Centimeters (cm)

Feet (ft) Meters (m)

Yards (yd) Kilometers (km)

Miles (mi)

How many square units make up the area of this rectangle?

Often, not all of the sides are given. You need to calculate the missing sides.

In a parallelogram, opposite sides are equal in length. 10 ft. 4 ft. EQUILATERAL polygons – a polygon in which all of the sides have equal lengths P = P = P = P = P = P = P = P = P = P = P = P =

2 cm 5 in

6 ft

3 m

1 yd

4 cm

What is the perimeter of a rectangle with a length of 8 cm and a width of 5 cm?

What is the perimeter of a parallelogram with one side of 5 ft. and the other side

of 3 ft.?

What is the perimeter of an equilateral triangle with a length of 8 inches?

Calculating Perimeter of Complex Shapes

Add up all the sides. You may have to figure out some of the missing sides first.

P = ___ + ___ + ___ + ___ + ___ + ___ + ___ + ___

P = _______ ft

8 ft

10 ft

2 ft

2 ft

2 ft

P = ___ + ___ + ___ + ___ + ___ + ___ + ___ + ___ + ___ + ___ + ____ + ___

P = _________ units

Area

Parallelogram

A = bh A = bh

A = 7 x 4 A = 4 x 9

A = 28 sq. in. A = 36 cm2

Area of a Parallelogram = base x height

Triangle

A = ½ bh A = ½ bh

A = ½ x 4 x 3 A = ½ x 6 x 4

A = 6 cm2 A = 12 sq. ft.

Area of a Triangle = half x base x height ~or~

Area of a Triangle = base x height / 2

7 in

4 in 4 cm 5 cm

9 cm

3 cm

4 cm

5 cm

6 ft

5 ft 5 ft 4 ft

Units used to describe area:

(Square Units)

Customary: Metric:

Square Inches (sq.in.) Centimeters Squared (cm2)

Square Feet (sq. ft.) Meters Squared (m2)

Square Yards (sq. yd.) Kilometers Squared (km2)

Square Miles (sq. mi.)

Finding area using squares on a grid:

Area = ___________ square units

Area = ______ square units Area = _______ square feet

Calculate the area:

Volume

Volume of a cube

V = lwh

V = 2*2*2

V = 8 cm3

Volume = length x width x height

Volume of a rectangular prism

V = lwh

V = 6*3*4

V = 72 cm3

Units used to describe area:

(Square Units)

Customary: Metric:

Cubic Inches (cu.in.) Centimeters Cubed (cm3)

Cubic Feet (cu. ft.) Meters Cubed (m3)

Cubic Yards (cu. yd.) Kilometers Cubed (km3)

Cubic Miles (cu. mi.)

Calculate the volume:

volume = cm3

volume = cm3

volume = cm3

volume = cm3

volume = cm3

volume = cm3

volume = cm3

volume = m3

volume = mm3

volume = m3

volume = cm3

volume = cm3

Calculate the volumes for each of the objects below.

Length = 15 m Width = 6 m Depth = 2 m

volume = m3

Length = 25 cm Width = 9 cm

Height = 30 cm

volume = cm3

Length = 80 cm Width = 45 cm Height = 40 cm

volume = cm3

Length = 9 mm Width = 9 mm Height = 9 mm

volume = mm3

Length = 10 cm Width = 4 cm

Height = 15 cm

volume = cm3

Length = 15 m Width = 12 m Height = 14 m

volume = m3

Length = 120 mm Width = 30 mm

Height = 160 mm

volume = mm3

Length = 35 cm Width = 35 cm Height = 30 cm

volume = cm3

Find the volume of a cube with sides of 5 yards.

Find the volume of a rectangular prism with a length of 3 cm, a width

of 4 cm, and a height of 2 cm.

Find the volume.

A cube has a volume of 65 cubic inches. What is the length of its

sides?

A rectangular prism has a volume of 40 cubic feet. Its height is 2 feet and its width is 4 feet. What is its length?

Find the volume.

Find the volume.

Find the length of the missing side, if

the volume is 30 cubic inches.

Find the length of each side of the

cube if the volume is 27 cm3.

Shantae bought a box of Lucky Charms at the grocery store. She wondered what the volume was, so she decided to measure it. The length was 7 inches, the width was 2 inches, and the height was 9 inches. What was the volume?

Ron ships XBOX 360s to stores. He needs to know the volume of the boxes at the UPS store, so he knows how many XBOX 360s he can fit in there. The dimensions of the boxes at the UPS store are 4 ft by 3 ft by 4 ft.

Jerry is in charge of bringing dice to his math class for his probability unit. Each die is 1 cubic centimeter. If he needs to bring 20 dice (20 cubic cm) and has a box that has a base that is 2 cm by 5 cm. How tall does his box need to be?

7 in

7 in

7 in

3 in

3 in

8 in

3 cm

3 cm

1 cm 2 in

? in

5 in

Volume with cubes: