Area of a Triangle
"½ bh"
This video introduces the formula for the area of a triangle. The hook reminds students that the formula is 1⁄2 b x h. It explains how to find the base and height of a triangle in order to find the area and demonstrates why area is calculated this way, using the area of a parallelogram as a proof.
Triangle area, OK?
That’s just 1⁄2 b x h,
And we get it every day and night,
1⁄2 times the base and height. (2x)
A triangle is a three-sided shape,
That can be different, they don’t look the same.
Whether it’s equilateral, isosceles or scalene,
To find the area, you just do the same thing.
First find the base, pick any side,
Usually we pick the long one though, that’s alright.
The length of the base, we’ll call that b,
Now we need the height, and then you see.
The height is the distance from the base
To the top of the triangle. But wait,
It has to be measured at 90 degrees,
Don’t go drawing random lines all around - that’s weak.
So the height might be in the middle of the shape,
or outside the shape or the side, OK?
Either way, you see the height is h.
Next up, the formula is what I might say, hey:
Triangle area, OK?
That’s just 1⁄2 b x h,
And we get it every day and night,
1⁄2 times the base and height. (2x)
Let’s see why it’s this way,
It’s not just random, that’s insane.
Take your triangle, make a copy please,
Then rotate that at 180 degrees.
Put them together, and what do we see?
That’s a parallelogram, boy easy,
Now let’s keep it going, alright?
Slice the triangle right at the height,
Put it on the other side, too hot to handle,
Look at this, we just formed a rectangle.
Yeah, that’s a simple shape,
The area of that would be b times h,
So the one triangle is just half that,
I’ll break down these facts and leave 'em in a cast.
Keeping digging if you need more info,
Flocabulary, making math so simple.
Triangle area, OK?
That’s just 1⁄2 b x h,
And we get it every day and night,
1⁄2 times the base and height. (2x)
The area of a triangle is 1⁄2 b x h. That is one half of the triangle's base multiplied by its height. If you're looking for the quick formula, now you have it. Enjoy it! But if you want to become a triangle superstar, this song will show you exactly how to use the formula, and also explain to you why this formula works.
The area of a triangle is 1⁄2 b x h. That is one half of the triangle's base multiplied by its height. If you're looking for the quick formula, now you have it. Enjoy it! But if you want to become a triangle superstar, this song will show you exactly how to use the formula, and also explain to you why this formula works.
There are three types of triangles, and the area formula works for all of them. You can determine which type of triangle you're looking at by measuring the sides or angles. In an equilateral triangle, all three sides and all three angles are equal. An isosceles triangle has just two equal sides and two equal angles. And in a scalene triangle, all sides and angles are different.
There are three types of triangles, and the area formula works for all of them. You can determine which type of triangle you're looking at by measuring the sides or angles. In an equilateral triangle, all three sides and all three angles are equal. An isosceles triangle has just two equal sides and two equal angles. And in a scalene triangle, all sides and angles are different.
To begin finding the area of the triangle, you need to find the base. Don't let the name deceive you though. Unlike the base of a building or a cheerleading pyramid, the base of a triangle doesn't have to be on the bottom. The base can actually be any side. So pick one, but just make sure you remember which one you picked.
To begin finding the area of the triangle, you need to find the base. Don't let the name deceive you though. Unlike the base of a building or a cheerleading pyramid, the base of a triangle doesn't have to be on the bottom. The base can actually be any side. So pick one, but just make sure you remember which one you picked.
Once you choose your base, it's time to measure the height. To find the height, draw a perpendicular line from the base to the highest point in the triangle. Perpendicular means that it is 90 degrees from the base. It also means that it will just look like a T.
Once you choose your base, it's time to measure the height. To find the height, draw a perpendicular line from the base to the highest point in the triangle. Perpendicular means that it is 90 degrees from the base. It also means that it will just look like a T.
As this picture shows, sometimes when you draw the line for height, it will be outside of the shape. This won't ever happen if you choose the longest side to be your base though.
As this picture shows, sometimes when you draw the line for height, it will be outside of the shape. This won't ever happen if you choose the longest side to be your base though.
Once you find the base and height, finding the area is easy. It's just 1⁄2 b x h. Let's do an example. The base of your triangle is 7 inches, and the height is 10 inches. So:
Area = 1⁄2 b x h
Area = 1⁄2 7 inches x 10 inches
Area = 1⁄2 70 inches2
Area = 35 inches2
Once you find the base and height, finding the area is easy. It's just 1⁄2 b x h. Let's do an example. The base of your triangle is 7 inches, and the height is 10 inches. So:
Area = 1⁄2 b x h
Area = 1⁄2 7 inches x 10 inches
Area = 1⁄2 70 inches2
Area = 35 inches2
Now you know the formula. But we'll go further and tell you why this formula works.
If you put two identical triangles together base to base, you'll always get a parallelogram. That's a shape that has two sets of parallel sides. So the area of one triangle will be half the area of the parallelogram you get by doubling it. But what is the area of a parallelogram?
If you put two identical triangles together base to base, you'll always get a parallelogram. That's a shape that has two sets of parallel sides. So the area of one triangle will be half the area of the parallelogram you get by doubling it. But what is the area of a parallelogram?
The area of a parallelogram = base x height. We can show this by slicing the parallelogram at the height and moving the sliced area to the other side. This will always give us a rectangle. We haven't changed the area of this shape (we've only moved it around). And we know a rectangle's area is base x height. So a parallelogram's area = b x h. And a triangle's area is half of that. Thus, a = 1⁄2 b x h.
The area of a parallelogram = base x height. We can show this by slicing the parallelogram at the height and moving the sliced area to the other side. This will always give us a rectangle. We haven't changed the area of this shape (we've only moved it around). And we know a rectangle's area is base x height. So a parallelogram's area = b x h. And a triangle's area is half of that. Thus, a = 1⁄2 b x h.
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