# Area, Perimeter, Volume

## Introduction

Perimeter is the measurement of the distance around an object.

Area is the measurement of 2D space inside an object.

Volume is the measurement of 3D space inside an object. ## Perimeter and Area Examples ### Example 1: Rectangles!

How do we measure perimeter?

A rectangle has 4 sides. Opposite sides have the same length. Take look at the image on the left. Measure and add up the all four side lengths! What do you get?

How do we measure area?

In a rectangle, area is determined by multiplying the width by the height. That means you take the two different sides and multiply them together. Remember, you only multiply two values, not four!

Make sure you watch out for UNITS!!!

Whether it be in cm, mm, ft, etc.

Perimeter will be the normal measurement, but area is the measurement SQUARED!

Area = 6cm * 2cm = 12 square cm

Perimeter = 6cm + 2cm + 6cm + 2cm = 16cm

### Example 2: Squares!

Fun fact, a square is just a rectangle with four identical side lengths!

Can you solve the problem on the right? Give it a go!

Area = 6cm * 6cm = 36 square cm

Perimeter = 6cm + 6cm + 6cm + 6cm = 24 cm  ### Example 3: Triangles!

For the perimeter, measure the three sides of the triangle and add them up!

Area is a bit more tricky!

For a triangle, the formula for area is 1/2 times the length of the base and the length of the height. (1/2 * b * h)

Can you figure it out? Give it a go, but watch for UNITS!

You can use a calculator for this problem!

Area = 1/2 * 45ft * 26ft = 585 square ft

Perimeter = 31 ft + 45 ft + 42 ft = 118 ft

## Volume Examples

### Example 1: Rectangular Prisms/Cuboids!

The volume is calculated by multiplying the base by the height by the width!

(b * h * w)

Watch out! The units will now be in CUBES because we are now in 3D!

Can you figure it out from the image on the right? Give it a try!

Yes, you can use a calculator, but try not to if you want a challenge!

Volume = 12 in * 6 in * 15 in = 1080 cube in  ### Example 2: L-shaped Challenge!

Tricky right? Well, not really!

Take the volume of the whole, bigger shape, and then subtract the rectangular prism that has been cut out.

Good luck! Use a calculator!

Volume:

60 mm * 80 mm * 10 mm - 40 mm * 60 mm * 10 mm = 24,000 cube mm