With Pi Day coming up on March 14, 2018, this is a good time to review the most important Geometry formulas that every student should learn in high school.

About Pi Day

But first, what is Pi Day – in case you don’t know about it. We don’t know who founded Pi Day, but it is a worldwide educational event, celebrated every year on March 14th,  that encourages teachers to engage in classroom activities that reinforce the fact that Pi can be used to calculate the area and circumference of circles, the volume of spheres, and other numbers that are related to two and three-dimensional shapes that are fundamentally circular.

Why is Pi Day held on March 14th? (Don’t be embarrassed if you don’t know, somebody had to explain it to us the first time we heard about it.) It is called Pi Day because March 14th can be represented as 3/14. And as you know, 3.14 are the first three digits of Pi, which is represented by the Greek letter π.  They are only the first three digits of Pi, which is the ratio of the circumference of a circle to its diameter. As you know, some students are fond of being able to recite from memory the value of Pi up to dozens or hundreds of digits to the right of the decimal point . . . 3.14159 and onward. (Smart students seem to think that they will get accepted by top colleges if they can reel off those numbers from memory. To our knowledge, this college admissions strategy has not been shown to work.)

Basic Knowledge of How to Use Pi

Apart from using Pi to show off, your students should understand these formulas that use the number.

  • πD (π x the diameter of a circle) or 2πR (π x twice the radius of a circle) will determine the circumference of a circle.
  • πR2 (π x the squared radius of a circle) will determine the area of that circle.
  • 4/3 x π x R3 (4/3 x π x the cubed radius of a sphere) will determine the area of a sphere.

The Pythagorean Theorem

Here’s another basic formula that every high school student should have under his or her belt.

  • A2 + B2 = C2 (the Pythagorean Theorem) is used to calculate the length of the hypotenuse of a right triangle. A right triangle is one in which the angle between two legs forms a 90ᴼ To get the length of the hypotenuse (the line that is opposite the right angle), you add together the squares of the lengths of the two sides that form the right angle. You then find the square root of that total to determine the length of the hypotenuse.

Finding the Area of Geometric Shapes with Straight Sides

This is pretty basic stuff, but it bears knowing.

  • Side2 is used to calculate the area of a square. If the side of a square is 4 inches, for example, the area of that square is 16 square inches, or 42.
  • Base x Height is used to calculate the area of a rectangle or a parallelogram. Weird, isn’t it, that the same formula works for either a rectangle or a parallelogram? When we were in school, we liked to ask, “What happens if you squash a parallelogram so it becomes just a line? Does the formula still work then?” Of course, it doesn’t. But we never found a geometry teacher who could tell us why. If you know the answer, please let us know.

Are the students you know fully able to use the very basic formulas we explain in today’s post? We encourage you to contribute your views by, Participating in a Student Research Foundation Career Pathway Study.

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