Question

Find the area of this triangle(picture of triangle in comments)
a. 2(square root)5 in^2
b. 80 in^2
c. 8(square root)5^ in^2
d. 48 in^2
e. none of these

Answer 1

For any triangle, it is \(\dfrac{1}{2}bh\). So if you know or can find the base and the height, it is easy.

Answer 2

i know the formula, when i used the formula and did the math i got 18 as the area?

Answer 3

Ah, if you only have sides, there are a few other options.

Answer 4

okay, can you tell me what my other options are possibly?

Answer 5

@C0stell0

Answer 6

Well, because it is isosceles it is pretty easy to get the height.

How did you get 18?

Answer 7

i think i just used 6 as my height?

Answer 8

Ah, that would be wrong. It is not a 45-45-90 triangle.

Have you used the Pythagorean theorem to solve parts of a right triangle before?

Answer 9

no, i've not tried that one before

Answer 10

Ah, for any right triangle where the legs are a and b and the hypotenuse is c:
\(a^2+b^2=c^2\)

Answer 11

so in this case it would be

Answer 12

?

Answer 13

Now, how do we get a right triangle in yours? Well:

Cut it in half! This only works because the sides are both 6, so we know cutting it in half makes 2 right triangles with a hypotenuse of 6 and a leg of 4 (half 8) and a leg of unknown length.

Answer 14

okay

Answer 15

So, can you fill out the \(a^2+b^2=c^2\) from that?

Answer 16

would it be 6^2+4^2=8^2 ? i'm still a bit lost. it looks like it's leading up to 48in^2 though? am i at least getting close to that?

Answer 17

Well, not quite. You have an unknown. Because we will be using b for base, I'll use a for the unknown.



\(a^2+4^2=6^2\)