Students sometimes think, "Oh no! Formulas! I hate formulas!" But really, formulas are designed to make life easier for you. Because if you didn't have a formula to use, you'd have to do a lot more work to get an answer. Formulas can help us do a wider range of problems. Here are a few formulas, with explanations:

P = 4s

The perimeter of a square is 4 times the length of a side.

P = 2W + 2L

The perimeter of a rectangle is twice the width plus twice the length.

F = 1.8C + 32

The temperature in Fahrenheit is 1.8 times the temperature in Celsius, plus 32.

d = rt

Distance traveled is the rate (speed) times the amount of time traveled.

A = 1/2(bh)

The area of a triangle is one half the base times the height.

C = 2πr

The circumference of circle is two times pi times the radius.

A + B + C = 180

The sum of the measures of the angles in a triangle is 180 degrees.

Here are some sample problems. These problems use the formulas shown above.

Sample #1

If the perimeter of a square is 48 units, what is the length of a side?

Solution #1

P = 4s, so 48 = 4s, and the answer is s = 12

Sample #2

A car travels 400 miles in 5 hours. How fast is it driving?

Solution #2

d = rt, so 400 = 5r, so r = 80

1.

The side of a square is 15. What is the perimeter?

2.

If the temperature is 50 degrees F, what is it in Celsius?

3.

If the width of a rectangle is 10, and its perimeter is 50, what is its length?

4.

At what temperature are the Celsius reading and the Fahrenheit reading equal?

5.

If the area of a triangle is 42 square units, and its height is 7 units, what is the length of its base?

6.

If a car travels 200 miles at a rate of 40 mph, how long did it take?

7.

The circumference of a circle is 50.26548. What is its radius?

8.

The width of a rectangle is 12 units, and its length is 4 less than its width. What is its perimeter?

9.

The angles in a triangle are x, 2x, and 3x. What is the measure of the triangle's largest angle?

10.

The angles in a triangle are x, x + 10, and 3x. What is the measure of the triangle's smallest angle?