Math Measurements - Classes & Resources

Formulas

The following formulas will help you with measuring linear measures, square measures and capacity measures. There are many math books that can help with this skill.

Perimeter of a Rectangle or Square:

Rectangle is a shape whose opposite sides are equal. The opposite sides are also parallel, which means that they are the same distance apart at all points.

To find the Perimeter of a rectangle, add all four sides.

Perimeter = length (L) + Width (W) + length (L) + width (W)

Another way to say this formula: p = 2 length (L) + 2 widths (W).

This method of finding a Perimeter will tell you the total of the outside measures of any rectangle.

Square is a shape that has all four of its sides equal. This means that the length and width of a square are the same. To find the perimeter of a square, you can say:

Perimeter = side + side + side + side.

You can also say that the perimeter of a square is equal to 4S. This means take the measure of one side times 4.

Example:

If a room is square and one side is 8 feet long:

1. write the formula: P = 4 x S
2. substitute the numbers: P = 4 x 8
3. solve the problem: P = 32 ft

The answer to this Perimeter problem = 32 feet. The formula used feet so the answer is in feet also.

Area of a Rectangle or Square

The flat surface of a rectangle or square is called an area. The Area of any figure is the number of square units it contains.

Area = Length times width, (A= L x W).

This means that the way to determine the area of a rectangle or a square is to take the length and multiply it by the width.

Example:

Find the area of a rectangle that measures 12 feet by 8 feet:

1. write the formula: A = L x W
2. substitute the numbers: A= 12 x 8
3. solve the problem: Area = 96 square feet or 96 ft²

The problem used feet, so the answer for area is also in square feet.

But area is counting the square feet. So, this means that the surface area of this rectangle is 96 square feet so if you are going to lay 1 foot square ceramic tiles, you will need 96 of them to cover this flat surface. Remember, the solution (the answer) for Area is always in square units.

Perimeter of a Triangle

The triangle is a closed, three sided geometric figure. The perimeter of any triangle is the sum of its three sides. An Equilateral Triangle has all three sides that are equal.

Perimeter = s + s + s

Example:

A certain Equilateral Triangle (all sides equal) has one side that is 10 feet:

1. write the formula: P = s + s +s
2. substitute the numbers: P = 10 + 10 + 10
3. solve the problem: P = 30 ft

The Perimeter of this Equilateral Triangle = 30 feet.

An Isosceles Triangle is a triangle that has two sides that are equal. The third side is different. Still, the above formula is used.

Perimeter = s + s + s.

Example:

A certain Isosceles Triangle (two sides equal) has the measures of 5 feet + 5 feet + 2 feet:

1. write the formula: P = s + s +s
2. substitute the numbers: P = 5 + 5 + 2
3. solve the problem: P = 12 ft

If all three sides of a triangle have different lengths, the triangle is called a Scalene Triangle. The above formula is the same for this Scalene Triangle:

Perimeter = s + s + s

Area of a Triangle

Any square or rectangle cut in half diagonally is a triangle, so remember that a triangle is 1/2 of a rectangle or 1/2 of a square.

We refer to the dimensions of a Triangle as Height and Base, not Length or Width.

A = 1/2 B x H ( 1/2 of the Base times the Height)

Another way to say it is that the Area of a Triangle is Base times Height, divided by 2.

Example:

A Scalene triangle has a base of 15 feet and a height of 12 feet.

1. write the formula: A = 1/2 B x H
2. substitute the numbers: A = 1/2 x 15 x 12

			( .50 x 15 x 12 is the Decimal way of saying it)
           Another way to say it: Area = 180 divided by 2 = 90. (the 180 is the answer to what 15 x 12 equals)

3. solve the problem: A = 90 ft²

The problem used feet, so the answer for area is also in square feet.

Formula For Volume:

Volume is the space enclosed (capacity) within a three -dimensional figure,such as a bin, a box, or a room. Volume is measured in cubic units (as in a cube).

Volume - length x width x height = Cubic unit.

V = L x W x H

Example:

A certain cube measures 10 x 15 x 4. To find out the total volume you have to know what the units of measure are! Is this inches, feet or cm or ??? Volume is measured in those cubic units, so multiply 10 by 15 by 4. The answer is 600 cubic units, whatever those are.

Solving Measurement Problems:

1. When measuring for any perimeter, area or volume, always round up to the next number. In this way you will not be "shorting" the customer of the necessary product to complete the job that he/she is doing. Example: If a customer wants to buy carpeting for his room that is 10.5 feet by 6.25 feet, you would be safe to round up to 11 by 7 feet to make sure that the customer has enough carpet to do the job. Never round down from the actual numbers.
2. When you have measurements that are in both inches and feet, you must turn them all into feet or a fraction or decimal part of a foot to do the math.

You cannot add or multiply inches and feet together. The answer will always be wrong.

Example: If I have something that is 8 feet and 4 inches wide.

1. I must turn it into 8.33 feet
2. OR I can turn it into 8 1/3 feet

If the other side of the dimension is 7 feet and 6 inches high

1. I can turn it into 7.5 feet
2. OR I can turn it into the fraction 7 1/2 feet