Answer:
area is 192, h is 16.
Explanation:
First, split the triangle down H to get two right triangles, this is so we can find H. The bottom line is now 12 inches, while the right side is still 20. Attached picture shows what I mean.
Next, use the pythagorean theorem to find H. The pythagorean theorem is a^2 + b^2 = c^2, where C is opposite the right angle (Pythagorean theorem ONLY works on right triangles.). a is the unknown in theorem, H is your unknown, a = H.
b^2 = 12^2 = 144
c^2 = 20^2 = 400
Now, plug in our variables to the theorem.
a^2 + 144 = 400.
Isolate the variable.
a^2 = 256.
find the square root of both sides.
a = 16.
Now, we know H is equal to 16. All that's left is to use the equation for area of a triangle: area = 1/2(base*height)
area = 1/2(24*16)
area = 1/2(384)
area = 192.
Remember, Pythagorean theorem is ONLY useful on right triangles! I wish you luck in geometry! :)