How To Find Area Of A Triangle
Question
What is the reason for multiplying by one half when finding the area of a triangle?
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How To Find Area Of A Triangle

In this video, I'm going show you how to calculate the area of a triangle. There are two ways to calculate the area of a triangle, a simple way and a slightly more complicated. So, I'll start with the simple way. There is a simple formula to work out the area of a triangle. The area of a triangle is the base times the height divided by 2. Half times b times h is what you often see. It's a half base times height. Okay, so the way to calculate the area of a triangle is you draw the triangle. Let's say it looks like that. And what I need to do is the height is not this length. It's not this length; it's the perpendicular height from this base. Let's call this one, the base, and what we need to do is find the height of this triangle which is perpendicular to the base, i.e. this line here. That's perpendicular that shows it is a right angle. So, it's this height. So, let's say the height is ten and the base is fifteen and the area is a half times ten times fifteen which is seventy-five. If these are centimetres, then it would be centimetres squared. Now, what is the reason for a half times the base times the height? If you think about the area of a square that's this, that's a square, the area of a square is simply the base times height. So, why is a triangle half of that? Well, if I draw that line that shows that area, I've split this area into two. So, the area is a half times the base times the height. That's the reason we use this formula half times base times height to figure out the area of a triangle. Now, that's one way of figuring it out but there is a slightly more complicated way. So, the slightly more complicated way of finding the area of a triangle is this. Let's say we have a triangle that looks like this but all you know is this length is ten, this length is eight, and you know this angle here - that's it. It's thirty degrees, so there is another formula for a triangle slightly more complicated which is this. Area is a half times a times b times sin c. Now, this basically means a half times this length times this length times the sin of this angle. So if we label this a, this b, and this length c, little c, little a, little b, then this angle, you label it opposite. So, this will be capital A, this is b so capital B and this is capital C. This is why we put thirty into here. The area is a half times a which is eight times b which is ten times the sin of big C so it's the sin of this angle which is thirty. Now, sin of thirty is a half, so this is a half times eight times ten times a half. So, that is going to be twenty centimetres squared and when you enter it into your calculator, you will get twenty. That's how to calculate the area of a triangle. .