Measurement: Area, Perimeter, Volume!

The audience that this mind map is targeting is students towards the end of elementary and early middle school. This will be used as a tool to help students understand how to do area, perimeter, and volume. This would be a resource they could use on homework so that they can get help threw games, videos, and a step by step means. To get the full affect you start with area vs perimeter, then move to area, then perimeter, and lastly volume.

Area vs Perimeter

These two measurements can seem similar but they are very different! To see the difference lets watch the video that is attached.

Terms

The base is represented by the letter b. Which is the bottom of the shape.

Height is represented by the letter h and measures how tall the shape is.

Radius is represented with the letter r and is any straight line that can be drawn from the center of the circle. Also the radius is one half the diameter.

Diameter is represented by the letter d and is a line that touches two points on the circle but this line must go through the center.

Pie is a term that represents a number that goes on forever. We would have a hard time multiplying a bunch of numbers so we shorten pie to 3.14.

Volume

The amount of space a three dimensional shape takes up or occupies. We see volume in our daily lives and the most common object that we see this in is a bottle of soda. This is because the people who make these bottles have to know the volume to be able to fill up all of their bottles the same way.

Rectangular Box

For a rectangular box (or commonly known as a rectangular prism) we will need to find the Area of the base and the height of the box. To find the area of the base we use the area formula of a rectangle which is length times width. Watch the attached video for an example.

First find the area of the base. Which is length times height

Then times that number by the height.

Right Cylinder

The formula for this is the exact same as a rectangular box. Which is the area of the base times the height. In this case you will need to find the area of the circle on the bottom which is the radius squared times pie. Watch attached video for an example.

First find the area of the base. Which is the area of a circle.

Then multiply that number by the height.

Volume of a Pyramid and Cone

This is similar to the other two because like the other two we need to find the area of the base, which for a pyramid is a square and a cone is a circle. then we multiply the area of the base by the height and divide by 3. The formula looks like 1/3 Area of the base times the height. Watch attached video for an example.

Pyramid

First find the area of the base. Which is the area of a sqaure

Then multiply this number by the height.

Lastly divide by three.

Cone

Find the area of the base. Which is the area of a circle.

Multiply by the height.

Then divide by three.

Area

The amount of space inside a flat object or shape. Such as, a square or triangle.

Square or Rectangle

When looking at area of a square or a rectangle you need to find the length and the width. Once we have both of these number we multiply them. The formula looks like length times width.

Do I have Lenth

Do I have Width

Now Multiply the Two

Parallelogram

For a Parallelogram we need to know two things the base (b) and the height (h). A parallelogram is named this way because it consists of two pairs of parallel lines. For an example watch the video that is attached. The formula is base times height.

Do I know the base

Do I have the Height

Multiply the two

Triangle

For a triangle you will need to have the same measurements as a parallelogram the only difference is that you want one half of the product of these two. The formula looks like 1/2 length times height.

Do I have the base

Do I have the height

Multiply the two

divide by two

Trapezoid

For a trapezoid you will need to know three measurements. you need to have the base, the top (more commonly known as the second base), and the height. Then like the triangle you will need one half of the total product. For an example watch the video that is attached.The formula is (a+b) times height divided by 2.

First find the measurements of the two bases

Then find the average of these two numbers

Multiply this by the height

Circle

For a circle we need to know two main terms. r or radius and pie (which equals 3.14). To find the area we must square the radius (or times the radius by it's self) and multiply by pie. The formula is radius squared times pie.

First find the radius

Then square the radius

Multiply this product by pie or 3.14

Perimeter

The total distance around a two dimensional flat shape. To calculate perimeter we are adding all of the measurements around a shape together. Perimeter measurements for a circle change so lets look at the next box!

Circle

This is more commonly referred to as the circumference. You will need to find the radius, and from there you will multiply it by 2 and then multiply by pie (3.14).

First find the radius. The radius is one half the diameter

Then multiply that number by 2

Lastly multiply this by pie or 3.14

All other shapes

For all other shapes including squares, rectangles, and triangles we add up all the sides and we have the perimeter.

Add up all the sides of the shape