Basic Geometry Formulas for Beginning Students

Just starting out in geometry? Need some help solving geometry problems? Read on to learn about some of the basic geometry formulas that you'll use to find the perimeter, area and circumference of shapes.

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Geometry Formulas for Beginners

In geometry, you'll use formulas, which are also called equations, to solve problems. Geometry problems often give you information about a shape, like how tall or wide it is, and then ask you to put that information into the correct formula to find the right answer.

Types of Geometry Formulas

Some geometry formulas are used to find a shape's perimeter, which is the distance around the outside of the shape. For example, if you measured the distance all the way around the block you live on, that distance would be your block's perimeter. If a shape has sides that are all straight lines, you can find its perimeter by adding the lengths of the sides together. For circles, the perimeter is called its circumference.

Other geometry formulas are used to figure out the area of shapes. The area is all of the space inside a 2-dimensional, or flat, shape. For example, if you wanted to know how big a park or a football field was, you would measure its area.

Basic Geometry Formulas Explained

Perimeter of a Square

Squares are shapes with four equal sides. The formula for finding the perimeter of a square can be written like this:

P = 4s

'P' represents the perimeter, and 's' represents the length of a side. The term '4s' tells you to multiply the length of one of the square's sides by four. If the length of one side is five inches, you would multiply five times four to get a perimeter (or 'P') of 20 inches (5 x 4 = 20).

Tip: In math equations, you'll often see a number right next to a letter, like '4s.' When you see this, you multiply the number and the value of the letter together.

Perimeter of a Rectangle

Rectangles have two longer parallel sides and two shorter parallel sides. To find the perimeter of a rectangle, you use this formula:

P = 2L + 2W

In this formula, 'P' represents the perimeter of the rectangle, 'L' represents the length of one of the long sides of the rectangle and 'W' represents the width of one of the short sides of the rectangle. This formula tells you to multiply the length by two and the width by two, and then add those results together. For example, if L = 5 meters and W = 3 meters, then the equation would be P = (2 x 5) + (2 x 3). If you solve this equation, you'll find that this rectangle's perimeter is 16 meters.

Tip: The order of operations tells us to multiply before adding when we simplify expressions. That's why we multiplied two times five and two times three first, and then added the resulting numbers together.

Area of a Square

Remember, area is the amount of 2-dimensional space covered by a shape. Here is the formula you'll use to find the area of a square:

A = s^2

In this formula, 'A' represents the square's area and 's' represents the length of one of the square's sides. The value of 's^2' is equal to the length of one side to the second power. For example, if the square's sides are each three centimeters long, its area is equal to three centimeters to the second power, or nine square centimeters.

Tip: 'To the second power' means 'the number multiplied by itself.' For example, four to the second power equals 16 (4^2 = 16) because four times four equals 16 (4 x 4 = 16).

Area of a Rectangle

Need to find the area of a rectangle? Here's how you write the formula:

A = L x W

In this formula, 'A' means 'area,' 'L' means 'length' and 'W' means 'width.' You find the area of the rectangle by multiplying its length by its width. For example, if the rectangle is eight inches long and six inches wide, you multiply eight times six to get the area of 48 square inches (8 x 6 = 48).

Circumference of a Circle

Circumference is the distance around a circle. Use this formula to calculate circumference:

C = 2(pi)(r)

The 'C' in this formula stands for 'circumference,' and the 'r' stands for 'radius.' Pi has a value of 3.14. The formula tells you that to find the circle's circumference, you multiply two times 3.14 times the length of the circle's radius (C = 2 x 3.14 x r). For example, if the radius of the circle is ten centimeters, you multiply two times 3.14 times ten to find the circumference (C = 2 x 3.14 x 10). When you multiply these three numbers together, the result is 62.8 centimeters.

Tip: The radius is the distance from the center of the circle to the edge of the circle. It is equal to half of the circle's diameter. For that reason, this formula can also be written like this: C = (pi)(d), where d = diameter.

Area of a Circle

Just like squares and rectangles, circles have areas as well. Here's the formula for finding the area of a circle:


'A' represents the area of the circle, and 'pi' equals 3.14. The term 'r^2 ' represents the value of the radius to the second power. To find the area, multiply 3.14 by the value of 'r^2,' which is 'r' times itself (A = 3.14 x r x r). For instance, if the radius of the circle is four meters, you multiply 3.14 times four times four to find the area (A = 3.14 x 4 x 4). The result is 50.24 meters.

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