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

1 Answer
Oct 9, 2015

The area would be 120 ft^2120ft2

Explanation:

Pythagorean Theorem says this for triangle side lengths:

a^2 + b^2 = c^2a2+b2=c2
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 = 26^2242+b2=262
576 + b^2 = 676576+b2=676
b^2 = 100b2=100
b = 10b=10

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

1/2bh = A12bh=A

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

1/2(10)(24) = A12(10)(24)=A
240/2 = A2402=A
120 = A120=A

Put your units on (ft^2ft2) and you get the answer at 120 ft^2120ft2
Hope this helped!