Area of a Right Triangle

      

    This is a right triangle. Why is it called a right triangle you may ask? This is because of the fact that the triangle contains a right angle (in the bottom left). To find this shape's area you cannot just multiply 3 units by 4 units by 5 units, which would give you 60 cubed units(which is definitely not the answer). One reason why this is wrong is because your answer comes in "cubed units", which you only use for 3D shapes, such as a cube. You want your answer to come out in "squared units", which you use for 2D shapes, such as a square.

    However, you may have noticed that by flipping the triangle over the hypotenuse (the longest side), you will make a square with side lengths of 3 units and 4 units. This is very useful information for finding the area of the triangle.

    As you can see, this rectangle is made up of two right angle triangles, each with side lengths of 3 units, 4 units, and 5 units. Because the rectangle is made up of two right angle triangles, the area of the rectangle is twice as much as the area of one right angle triangle. This also means the area of the rectangle divided by 2 is equal to the area of 1 right angle triangle. We can use this to find the area of one right angle triangle by finding the area of the rectangle and dividing that by two.

    3 units times 4 units is 12 square units, and 12 square units divided by 2 is 6 square units, or the area of a right angle triangle with the side lengths of 3 units, 4 units, and 5 units! Good Job! You just found out how to find the area of a right angle triangle!

    But, you may be thinking, "Well, this method is great, but still, it takes too much time to come to an answer." However, this method is only the foundation of finding the area of any triangle, whether it is scalene, isosceles, obtuse, equilateral, or acute. First off, let me tell you the variables we'll be using. Take two sides that do not include the hypotenuse. Two examples include the side with a side length of 3 units and the side with a side length of 4 units from the examples above.  Let's call these two sides L and W.

    Now that we know all the variables, I'll tell you the formula and explain to you how it works. The formula is L times W divided by 2. The L times W represents multiplying the two sides of the newly made rectangle. These sides first started off as sides of the right angle triangle, but then became sides of the rectangle. Because we multiply these sides early on, we must also divide the answer by two. When we multiply the two sides early on, we multiply them as if they are sides of the rectangle, even though they are not. This is also why we must divide them right after we multiply them.

    So now you know how to find the area of a right angle triangle through a formula and through a basic strategy! Great Job! But, don't use this strategy to find the area of any triangle that is not a right angle triangle, because it will not. This is why I challenge you to find a different formula to find the area of any triangle using the formula I taught you today.