Math Made Easy! Find the Area of a Triangle

• Area of a Circle
• Circumference of a Circle
• Surface Area of a Cylinder

Area of a Triangle

One of the first "area" concepts that geometry students learn is how to find the area of a square and rectangle. This geometry concept is quickly followed by how to find the area of a triangle.

The subject of geometry often poses two challenges for high school geometry students:

1. how to remember all the formulas, and
2. how to visualize the geometry problem

The trouble many math students have, however, is once the "memorized" formula is forgotten while taking a test, all hope of solving the area problems is gone! The best way too avoid this situation is to understand the formula in the first place; afterall, it is much easier to remember a concept than it is to remember formulas with no meaning attached to them.

For example, in order to remember the area of a triangle equation think of a peanut butter & jelly sandwich! Read on if you would like to know what pb &j has to do with 1/2 bh ...

A = 1/2bh

Where: b is the base and h is the height

This formula seems simple enough, and may not even be troublesome to recall while taking a quiz that just covers the area of triangle, but recall difficulties often occur while taking tests that cover multiple concepts. A test on the area of shapes will require the memorization or recall of multiple equations for multiple shapes. And it is rote memorization that very often leads to mathematical mistakes.

Therefore, the best way to remember an equation is not to memorize it, but to understand what the equation means or to picture it in your head. Read the Math Made Easy! Triangle Tip below for ways to do this for the area of a triangle equation.

So, what does a peanut butter and jelly sandwich have to do with remembering the equation for the area of a triangle forever?

• Question: How many ingredients does it take to make a peanut butter and jelly sandwich?
• Answer: 3
• Question: How many sides does a triangle have?
• Answer: 3

So, when attempting to recall the area of a triangle equation, visualize a peanut butter and jelly sandwich, noting that a pb & j is associated with a triangle because of the number 3.

Now, cut the peanut butter and jelly sandwich in half on the diagonal. Notice there are two triangles.

In the most simplistic terms, the area of a whole peanut butter and jelly sandwich is the area of a square (more or less), and the area of half of the sandwich (a triangle) is therefore half of the whole area. In other words, the triangle's area equals half of the square's area.

The area of a square is found by multiplying width times length. The area of a triangle is found by taking 1/2 of the triangle's width (called its base) times the triangle's length (called its height).

Assume a peanut butter and jelly sandwich is a perfect square. If the length of the pb & j is 1 unit and the width is 1 unit then we know the area of the whole pb & j is 1 sq. unit. It is therefore logical that the area of 1/2 of the sandwich is 1/2 sq. unit.

Let's look at a real peanut butter and jelly sandwich:

The area of the whole (square) pb & j:

• Area of square = (width) x (length)
• Area of whole square sandwich = (4) x (4)
• Area of whole square sandwich = 16 sq. inches

The area of 1 triangle piece of a pb & j:

• Area of triangle = (1/2)x(b)x(h)
• Area of triangle half of sandwich = (1/2) x (4) x (4)
• Area of triangle half of sandwich = 8 sq. inches

Just remember, a triangle is half of a square or rectangle, so the formula for finding the area of a triangle is like taking half of the area of a square or rectangle. Can you visualize it? Take another look at the equation for finding the area of a triangle:

Area of Triangle = 1/2(base)(height)

Really, it is just like taking 1/2 of the area of a square or rectangle, making it a very easy equation to recall on a test full of other area equations.

Note: The equation for the area of a triangle works for all types of triangles, not just right triangles (triangle with a 90 degree corner).

Before you even read the first question on a geometry test, write down all the formulas that the test covers on the top of the test to use as a reference.

This way, if confusion and frustration start to occur while facing a difficult question, the formulas will not be forgotten since they were written down before encountering a challenging problem.

Below you will find two typical geometry problems and their solutions for finding the area of different types of triangles.

Problem: Find the area of a triangle with a base of 6 cm. and a height of 3 cm.

Solution: Since b (base) and h (height) are known, simply plug the numbers into the formula:

• A = 1/2bh
• A = (1/2)(6)(3)
• A = 9

Answer: The area of a triangle with a 6 cm. base and a 3 cm. height is 9 sq. cm.

Problem: Find the height of a triangle with a base of 2 in. and an area of 6 sq. in.

Solution: Since A (area) and b (base) are known, simply plug them into the area of a triangle formula and solve:

• 6 = (1/2)(2)(h)
• 6 = (1)(h)
• h = 6

Answer: A triangle with a base of 2 in. and an area of 6 sq. in. has a height of 6 in.

Are you stumped on a homework problem for finding the area of a triangle? If so, go ahead and ask for help in the comment section below.

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