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

Question

1801 views around the world

You can reuse this answer
Creative Commons License

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!