Area of a Triangle

Once you’ve mastered the area of a rectangle and square (A=BH) it’s time to move onto the area of a triangle. The good news is, just like most things in math, the area of a triangle formula just makes sense! Two triangles together make up a square or rectangle so the formula for area of a triangle is simply half the area of a rectangle or square. Not quite tracking with us? No worries! Read on and we’ll spell it out clearly.

The Connection Between Squares, Rectangles and Triangles

Take a look at any square or rectangle and you’ll find two triangles hidden inside. Take any rectangle and simply draw a straight line from corner to corner. You’ll find yourself with two congruent (same size) triangles! This knowledge is especially helpful when it comes to finding area because, as we said earlier, you likely already know how to find the area of a rectangle, right? And, as you can now see, a rectangle is simply to triangles put together. Therefore, a triangle is half of a rectangle. Which means the area of a triangle is exactly half the area of its rectangle! Armed with this newfound knowledge, we’ll bet you can already find the area of a triangle even without us teaching you the formula.

Area of a Triangle Formula

Now that you understand that two triangles make up a rectangle this formula is unlikely to surprise you.

The formula for area of a triangle is simply this:$$A=\frac{(BH)}2$$

Notice anything familiar about that formula? That’s right, it exactly the formula for area or a rectangle and then, the whole thing is divided by two! Remember those pictures you saw a second ago - when the rectangles were divided into two triangles? That right there is why this formula works. A triangle is half of a rectangle so the formula for the area of a triangle must be the formula for area of a rectangle divided in half!

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Let’s Practice

Now that you understand where the formula comes from and why it works let’s test it out by solving some area of a triangle problems.

Find the area of a triangle with a base of 5 cm and a height of 6 cm.

Alright, let’s think through the formula:

• We know the formula for area of a triangle is  $$A=\frac{(B\times H)}2$$
• In this problem the base or B is 5 cm and the height or H is 6 cm so we can substitute those values into the equation like so: $$A=\frac{(5\times6)}2$$
• Now we can simplify  $$A=\frac{(30)}2$$
• And simplify again  $$A=15$$
• So the area of this triangle is 15 square cm

You’ve solved your first area of a triangle problem. Not too bad, right?

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Let’s try another one.

Find the area of a triangle with a base of 30 in and a height of 18 in.

Let’s think this through. The formula for area of a triangle is  $$A=\frac{(B\times H)}2$$.

• I this problem B = 30 in and H = 18 in so we can substitute like this: $$A=\frac{(30\times18)}2$$
• Then we have to simplify A = 540/2
• And again A = 270
• So the area of this triangle is 270 square inches

Nicely done! You’re already becoming a pro. But what about when things get complicated??? Don’t worry, we’re just about to walk you through it.