Question 892698: how do I solve this? Area = 1/2 (6√2)(2√20)
thanks I got confuse.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! area of a triangle is equal to 1/2 * base * height
it appears that the base is equal to 6*sqrt(2) and that the height is equal to 2*sqrt(20), or vice versa. it doesn't matter which is which because you are multiplying everything together anyway.
your formula is area = 1/2 * 6*sqrt(2) * 2*sqrt(20)
you can use the commutative law of multiplication to make your formula look like this:
area = 1/2 * 6 * 2 * sqrt(2) * sqrt(20)
you can use the associative law of multiplication to make your formula look like this:
area = (1/2) * (6*2) * (sqrt(2)*sqrt(20))
the square root laws allow you to make sqrt(2)*sqrt(20) equal to sqrt(2*20)
your equation becomes:
area = (1/2) * (6*2) * sqrt(2*20)
simplify this to get:
area = (1/2) * 12 * sqrt(40)
use the associative law again to make your equation look like this:
area = ((1/2)*12) * sqrt(40)
simplify to get:
area = 6 * sqrt(40)
sqrt(40) is equal to sqrt(4*10) which is equal to 2*sqrt(10).
your equation becomes:
area = 6*2*sqrt(10)
simplify this to get area = 12*sqrt(10)
it can't be simplified any further than that since there are no perfect squares in sqrt(10).
your original equation was area = (1/2) * 6 * sqrt(2) * 2 * sqrt(20)
your final equation is area = 12 * sqrt(10).
if you simplified correctly, they should get you the same answer.
now you use your calculator to confirm that both equations will give you the same answer.
i did the calculations and confirmed that both equations give you the same answer.
the answer that both equations gave me is 37.94733192.
i'm not exactly sure what you were asked to do.
if you just needed an answer, you could have solved it directly using the calculator and gotten 37.94733192.
if you were asked to simplify the equation, then your simplified equation is area = 12*sqrt(10).
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