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Perimeter, , and

Perimeter is a measurement of . It is the distance around something. We use perimeter when a around a or any place that needs to be enclosed. In that case, we would the distance in feet, , or meters.

In math, we usually measure the perimeter of . To find the perimeter of any , we add the of the sides.

2 m 2 m P = 2 m + 2 m + 2 m = 6 m

2 m

3 ft.

1 ft. 1 ft. P = 1 ft. + 1 ft. + 3 ft. + 3 ft. = 8 ft.

3ft

When we measure perimeter, we always use units of length. For example, in the above, the is meters. For the above, the unit of length is feet.

PRACTICE!

1. What is the perimeter of this figure?

5 cm

3.5 cm 3.5 cm

2 cm

2. What is the perimeter of this figure?

2 cm

Area

Perimeter, Area, and Volume

Remember that area is the number of units that are needed to cover a .

Think of a backyard enclosed with a fence. To build the fence, we need to know the perimeter. If we want to grow grass in the backyard, we need to know the area so that we can buy enough grass seed to cover the surface of yard. The yard is measured in square feet. All area is measured in square units. The figure below represents the backyard.

25 ft.

The area of a square Finding the area of a square: is found by multiplying side x side. 1. Estimate: s x s 20 x 20 = 400+ sq. ft. 25 ft. Area = side x side 2. Calculate: s x s 25 x 25 = 625 sq. ft.

To find the area of a rectangle, we can simply multiply the length by the width. Example: If we needed to determine how much paint to buy to paint a in this classroom, we would have to figure out how many square feet were on the wall. When we measure the wall, we find that it is 12 feet across and 8 feet high. We can use a piece of graph paper to lay out a model of the wall. 12 ft.

8 ft. Area of Rectangle = l x w

How many square feet are on that classroom wall?

PRACTICE! 1. Find the perimeter and area of your desk. 2. Use a piece of graph paper to lay out a model of your desk.

Area of a Right Triangle

Perimeter, Area, and Volume

Finding the area of a right triangle might be a little more challenging.

The right triangle has two sides that we call the

Height and the . The dashed lines in the Height diagram show us that a right triangle is simply half of the rectangle that we make if we flip the triangle

Base along its third side. Right Angle

To find the area of the right triangle, we multiply the base by the height and then divide by 2. We divide by 2 because the triangle is half the rectangle. When we multiply base times height, it is the same as multiplying length by width.

Area = Base x Height 2

The area of the right triangle in the grid below would be:

A = 5 x 6 2 6 in (Height)

A = 30 2

A = 15 inches 5 in (Base)

1 We may also see this written as: Base x Height. 2

PRACTICE!

1. Find the area of the right triangle. 4 cm

2 cm

Volume

Perimeter, Area, and Volume

Volume is a measure of capacity or space. Capacity is the space inside a figure. For example, think of a rectangular box (which is really a rectangular ) that is measured in centimeters. Its volume is the number of centimeter that will fit inside the box. Cubic centimeters are represented by this symbol: cm3

We buy dirt, sand, and other outdoor materials in cubic units such as cubic feet, cubic yards, and cubic meters.

To find the volume of a rectangular solid, we multiply length x width x height. The formula for finding the Volume of a Rectangular Solid is l x w x h.

3ft

2ft

5ft V = l x w x h

V = 3 ft x 2 ft x 5 ft V = 30 ft3 or cubic feet

Many cardboard boxes are labeled with their capacity, or amount of space inside, so that we will know how much they will hold.

PRACTICE!

1. Find the area of the rectangular prism below.

2 cm

1 cm 3 cm

PRACTICE!

Perimeter, Area, and Volume

1. Which of the following would require finding the perimeter of something?

 Buying enough picture frame material to go around my school picture  Buying enough sand to fill my little sister’s sandbox  Buying enough paint to cover my wall  Buying enough fencing to go around the playground

2. Which of the following would require finding the area of something?

 Buying enough picture frame material to go around my school picture  Buying enough sand to fill my little sister’s sandbox  Buying enough paint to cover my bedroom wall  Buying enough fencing to go around the playground

3. Which of the following would require finding the volume of something?

 Buying enough picture frame material to go around my school picture  Buying enough sand to fill my little sister’s sandbox  Buying enough paint to cover my bedroom wall  Buying enough fencing to go around the playground

4. Try these practice problems! Remember to identify the units!

Description: Perimeter Area Volume

Square: s = 3 cm

Rectangle: l = 6 m w = 3 m

Triangle: b = 5 in h= 4 in

Rectangular Solid l = 2m w = 1m h = 4 m