Luas Segitiga

Area: An Origin Story

So we know that the area of a triangle is the product of its base and height divided by two: $$A_{\triangle}=\frac{1}{2}bh$$ But where does this formula come from?

Before we can think about triangles, we have to think about quadrilaterals. Read the explanation that is linked, then come read about triangles!

Triangles

So what does any of this quadrilateral stuff have to do with triangles?

Well, any triangle can be made into a parallelogram by taking a copy of that triangle and sticking the two triangles together in a way that preserves the original height of that triangle.

This means we have a parallelogram with the same base and height as our triangle and area exactly twice as large as our triangle. Since we know the area of a parallelogram ($bh$), we can simply divide this area by two to get the area of our triangle!

Thus, $A_{\triangle}=\frac{1}{2}bh$.

(This is a literal equation, by the way)!

Bonus: Try deriving the area for a trapezoid on your own by cutting off one tip of a triangle!

The area of a triangle is one half times its base times its height. $$A=\frac12bh$$

The definition of area can be found here. The area of a triangle can be found by using the following formula: $$\color{blue}{A} = \frac{1}{2}\color{purple}{b}\times\color{orange}{h}$$ where b=base and h=height. $\\$ The area of the triangle below can be found by following the following steps: $$\color{blue}{A}=\frac{1}{2}(\color{purple}{5}\times\color{orange}{3}) \\ \color{blue}{A}=7.5 \text{ units}^2$$

(Video) Area of a triangle

by Math Antics

The video above explains the formula of the area of a triangle. It also shows why it applies to all triangles.

$\large{\text{Summary}}$

The area of a triangle is: $$A=\frac{1}{2} (B\times H)$$ $B$ is the base: It can be any side of the triangle. $\\$ $H$ is the height: A line extending from the opposite vertex of the base and perpendicular to the base.

Example

Here we have a right triangle with its base and height denoted.

We determine which side of the triangle is the base. With the same triangle, we can have a different set of base and height:

Of course, the area will be the same!

In obtuse triangles, sometimes the height is outside of the triangle:

Try it!