00:01
In this first problem, you want to find the area of a triangle when you're given the lengths of all three sides.
00:05
Well, when you're given the lengths of all three sides, what we can do is we can use what's known as heron's formula to find the area.
00:12
So heron's formula says that the area for this triangle will equal to the square root of s times s minus a times s minus b, where a, b, and c are the sides of the triangle.
00:24
And s is a constant.
00:27
To find s, what we do is we add up all the sides and divided by two.
00:31
So first, we're going to find our s value.
00:33
So in this case, we're going to do 3 plus 6 plus 7 and we'll divide it by 2.
00:38
Well, 3 plus 6 is 9, 9 plus 7 is 16, and 16 divided by 2 is 8.
00:43
So now that we have s, we can go and substitute our values into our area formula.
00:47
So the area will equal to the square root of 8 times 8 minus 3 times 8 minus 6 times 8 minus 6, 7.
00:56
So now we're going to scroll down a little bit.
00:58
So the area will equal to the square root of 8 times, well, 8 minus 3 is 5, 8 minus 6 is 2, and 8 minus 7 is 1.
01:07
Well, 8 times 5 is 40, 40 times 2 is 80, and 80 so it's going to be the square root of 80.
01:14
So now we can go to our calculator.
01:16
We're going to do the square root of 80, and it looks like they want it around one place after the decimal.
01:20
So you'll find that the area for this particular triangle would be about 8 .9 square feet.
01:26
So looking at your answer choices, this would be choice c.
01:30
Is that third choice there.
01:32
All right.
01:32
So now, let's scroll down to your second question here...