Tips for Understanding Geometry Formulas

Are you having trouble with geometry formulas? Plenty of students need geometry help because they have a hard time with all those pesky shapes and angles. Luckily, once you understand some of geometry's basics, you'll have an easier time grasping some of the more advanced topics. Let's take a look at some of the basic formulas and find out what they mean.

Area of a Rectangle
The area of a shape is how much space it takes up.

  • Draw a rectangle on a piece of paper.
  • If you look at the rectangle, the space inside of its borders is its area.
  • Say the rectangle has a length of 8 feet and a width of 5 feet.
  • Divide the rectangle lengthwise into 5 rows, then divide it vertically into 8 columns, so that the area is filled with little squares.
  • How many little squares are there? The answer is 40. You just found the area.

There's an easier way to calculate the area without drawing the squares. Just take the length, 8 feet, and multiply it by the width, which is 5 feet. 8 x 5 = 40, so the area is 40 feet.

The area for a rectangle is its length multiplied by its width, which is usually abbreviated to Arect = lw.

Area of a Triangle

  • Take a look at the rectangle from the last example.
  • Draw a line from one corner of the rectangle across the middle to the opposite corner. Notice that the rectangle is now divided into 2 equal triangles.
  • To calculate the area of one of the triangles, you take the Base length, which is the short side (5 feet in this case), and multiply it by the Height, which is 8 feet, then divide the total in half. So we have 8 x 5 = 40, and 40/2 = 20. The area of one of the triangles is 20 feet.
  • We divided the rectangle in half, so the triangles both have an area equal to half of the rectangle-s area.Anytime you see a triangle, the formula for its area is one half the Base length times the Height, which is shown as: Atri = (1/2)bh.

Who Wants Pi?
Pi is very important to the study of geometry, specifically circles. It is a mathematical constant, which means its value will never change. It is always equal to 3.14, which is actually a number that's been rounded. Pi doesn't divide perfectly, so it's true value can be taken to an infinte number of decimal places.

Pi represents the ratio of any circle's circumference (the distance around a circle) to its diameter (the distance across a circle). To calculate the area of a circle, you'll need to take the radius, which is half of the diameter, and square it (multiply the number by itself), then multiply that number by pi.

For example, if we have a circle with a diameter of 6 feet, to calculate the area we just need to find the radius and plug it into the formula. 6 / 2 = 3 feet, which is the radius. 3 x 3 = 9. 9 x 3.14 = 28.26 feet, the area of the circle.

Most calculators include a symbol for pi that will automatically plug 3.14 into the equation so you don't have to type it over and over again.

These basic formulas are the basis for most geometry study. But why does area matter? Whether you're building a house, making a bottle of soda or just packing for a vacation, you need to know how much space you have to use. Otherwise, things won't fit right. If you can calculate area, you'll know how much room an object takes up and how much room it has inside.

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