How do you find the area of the triangle when 24ft tall and the hypotenuse is 26ft?

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Answer 1 · 2015-10-09T01:06:11

The area would be #120 ft^2#

Pythagorean Theorem says this for triangle side lengths:

#a^2 + b^2 = c^2#
c being the hypotenuse and a/b being the leg lengths

Therefore, we can plug in 26 for c, 24 for a, and solve for b, which will be the base.

#24^2 + b^2 = 26^2#
#576 + b^2 = 676#
#b^2 = 100#
#b = 10#

Now that we know the base length, and the height, we can use the area for a triangle:

#1/2bh = A#

Let's plug in the remaining variables and solve for the answer.

#1/2(10)(24) = A#
#240/2 = A#
#120 = A#

Put your units on (#ft^2#) and you get the answer at #120 ft^2#
Hope this helped!