Math Made Easy! Find the Area of a Triangle

Geometry Tutorial

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 ...


Equation for Area of Triangle

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.


Think of a PB & J Sandwich to Recall the Area of a Triangle

Associate a pb & j with a triangle - A pb & j has 3 ingredients and a triangle has 3 sides.
Associate a pb & j with a triangle - A pb & j has 3 ingredients and a triangle has 3 sides.
Assume the whole pb & j sandwich is a perfect square and let's find its area.
Assume the whole pb & j sandwich is a perfect square and let's find its area.
The width of the square is 4 inches.
The width of the square is 4 inches.
The length of the square is 4 inches, making the area of the whole square sandwich 16 sq. inches.
The length of the square is 4 inches, making the area of the whole square sandwich 16 sq. inches.
Cut the square sandwich in half to create two triangle halves.
Cut the square sandwich in half to create two triangle halves.
Assume the triangle half is a perfect triangle and let's find the triangle's area.
Assume the triangle half is a perfect triangle and let's find the triangle's area.
The base of the triangle (its largest width) is 4 inches.
The base of the triangle (its largest width) is 4 inches.
The height of the triangle (like the length of a square) is 4 inches. The triangles area is 1/2 of 16 or 8 square inches, making the area of a triangle 1/2 the area of its square.
The height of the triangle (like the length of a square) is 4 inches. The triangles area is 1/2 of 16 or 8 square inches, making the area of a triangle 1/2 the area of its square.

Math Made Easy! Triangle Tips

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).


Geometry Test-Taking Tip

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.


Source

Problems & Solutions: Area of Triangle

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


#1 Find the area of a triangle given its base and height

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.


#2 Find the height of a triangle given its base and height

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.


Do you need more homework help finding the area of a triangle?

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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Comments 13 comments

Lord De Cross profile image

Lord De Cross 5 years ago

Omg! I wish I could mark you as a HUB of the day...you took all that effort and time..is wonderful KTRAP!! as you know I have this small talent as yourself... but you topped the cake! Women will be women! LOL!

Theoremetically awesome!

lord


ktrapp profile image

ktrapp 5 years ago from Illinois Author

Thanks for making me laugh lord. (That sentence is actually sort of funny if you think of it in Biblical terms - but that's a different subject.)

It may be a "mom" thing. I always found that food was the best way to explain math to my kids, even when young. It all started with cookies and giving one kid 3 and another 2. That teaches the even and odd concept real fast to a kid who has less. Then we moved onto jelly beans for multiplication, pie or pizza for fractions and so on. Perhaps math teachers should just keep a pantry of foods kids love. I swear they learn faster and more permanently this way.

Thanks for your great comment and I shall be checking out more of your math hubs.


H A Kap profile image

H A Kap 5 years ago from Ohio

Aaaaa.... you make me hungry for more math.. and crunchy peanut butter


ktrapp profile image

ktrapp 5 years ago from Illinois Author

H A Kap - It's been awhile since I've had crunchy peanut butter - sounds good. "Hungry for Math" would have been a better title for this hub and my other math/food hubs.


H A Kap profile image

H A Kap 5 years ago from Ohio

I taught math for a long time and you wrote an enjoyable hub. what else do you do?


Arlene V. Poma 5 years ago

Auggggggggggggggggggggggggggggggggggggggggggggggggggggh!!!


ktrapp profile image

ktrapp 5 years ago from Illinois Author

H A Kap - Thanks again. I am mostly involved in website design.

Arlene - HaHa! It's just math!


homesteadbound profile image

homesteadbound 5 years ago from Texas

I always had trouble remembering the formulas during tests. But if I had had a hub to read with sandwich pictures making it appear so easy. You are right, understanding the concept removes the need to remember the formula. Great job!


ktrapp profile image

ktrapp 5 years ago from Illinois Author

Thank you homesteadbound. I think you stated that so much more concisely than I did in my hub - "understanding the concept removes the need to remember the formula." Perfect.


stephaniedas profile image

stephaniedas 5 years ago from Miami, US

This was my favorite equation to do in math class when I was in school, but i had completely forgotten about it. Are you a teacher? I think you could be great at it. Voted up and useful :)


ktrapp profile image

ktrapp 5 years ago from Illinois Author

Stephanie, It's funny how some people have a favorite math formula and others detest math altogether. I am not a math teacher, though I've always liked the subject a lot. I appreciate your kind words and vote.


stephaniedas profile image

stephaniedas 5 years ago from Miami, US

Actually, I've always detested math because it never came easy to me, but there were a few rare times that I remember enjoying it. Other than triangles, I've always loved doing circle equations and when I got into Chemistry, I loved calculating wavelengths and doing all of that atomic number stuff, though I hated the rest of chemistry. It is funny how random things can speak to us!


ktrapp profile image

ktrapp 5 years ago from Illinois Author

That's so true Stephanie. While I was not a big fan of Chemistry I did like balancing chemical equations.

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