What is the area of the triangle if 8 and 12 are a leg and hypotenuse?

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Answer 1 · 2016-01-26T19:52:24

#A=16sqrt5approx35.7771#

The area of a triangle is found through the formula

#A=1/2bh#

The important thing to know is that the base #b# and height #h# in a triangle are always perpendicular, meaning they meet at a right angle.

We know this is a right triangle, so the two legs meet at a right angle and are the base and height of the triangle.

However, we only know one leg and the hypotenuse, so we need to determine the length of the other leg.

According to the Pythagorean Theorem, which applies to right triangles with legs #a,b# and hypotenuse #c#,

#a^2+b^2=c^2#

We can put in what we know, since one leg is #8# and the hypotenuse is #12#:

#8^2+b^2=12^2#

We can solve this for #b#, the length of the missing leg.

#64+b^2=144#

#b^2=144-64#

#b^2=80#

#b=sqrt80#

#b=sqrt16sqrt5#

#b=4sqrt5#

We now have determined that the legs of the triangle are #8# and #4sqrt5#. Since these are the base and height of the triangle, the area is

#A=1/2bh#

#A=1/2(8)(4sqrt5)#

#A=4(4sqrt5)#

#A=16sqrt5#

#Aapprox35.7771#