Learn the Pythagorean Theorem and Its Application in Triangles for Students

As a student, learning math can be challenging, but the Pythagorean Theorem is one concept that you don't want to miss. The theorem is essential in understanding the relationship between a triangle's sides and is used in solving numerous mathematical problems. This article will show you how to use the Pythagorean Theorem to find the area of a triangle, what the theorem is, and why it's important to know it. BizzLibrary.com also offers a downloadable PDF of the Pythagorean Theorem for you to use.

What is the Pythagorean Theorem?

The Pythagorean Theorem relates to the sides of a right triangle. It states that the square of the hypotenuse (the longest side of the triangle, which is opposite the right angle) is equal to the sum of the squares of the other two sides.

In other words, if we denote the length of each side of a triangle as a, b, and c, where c is the hypotenuse, the Pythagorean Theorem formula is:

c² = a² + b²

How to Use the Pythagorean Theorem to Find the Area of a Triangle

Now that you know what the Pythagorean Theorem is, let's take a look at how to use it to find the area of a triangle.

First, identify the sides of the triangle. One of the sides must be the hypotenuse and the other two sides can be any of the remaining sides (i.e., the opposite or adjacent side to the right angle). Once you have identified the sides:

1. Use the Pythagorean Theorem formula to calculate the length of the hypotenuse, if it's not already given.
2. Use the formula for the area of a triangle, which is 1/2(base x height), to find the area of the triangle.

For example, if the length of the two legs of a right triangle are 3cm and 4cm, respectively, you can find the length of the hypotenuse by using the Pythagorean Theorem:

c² = a² + b²

c² = 3² + 4²

c² = 9 + 16

c = √25

c = 5cm

Now that you have calculated the length of the hypotenuse (c), you can find the area of the triangle:

A = 1/2(base x height)

A = 1/2(3cm x 4cm)

A = 6cm²

Get the Pythagorean Theorem PDF Download

Understanding the Pythagorean Theorem is essential for solving math problems, and we have made it easier for you with our downloadable Pythagorean Theorem PDF. Download it today and have access to print it out for use in class, homework, and study sessions. BizzLibrary.com is committed to providing students and educators with valuable resources that are easy to use and effective in learning.