Hi! This looks like homework...
so I can help!
What you would need to do first is find the height of the triangle, you know, the dashed line. 15 is the hypotenuse side length. Now we need to solve for a^2 + b^2 = c^2 (hypotenuse formula) a^2 = 10^2, and c^2 = 15^2. So now..
if a^2 + b^2 = c^2, then c^2 - a^2 = b^2. Just moving stuff around. :D
That would be 15^2 - 10^2 = b^2, which is 225 - 100 = b^2. The result is 125 = b^2.
ehaggghh it's a decimal
b^2 is 125... and b is 11.1803398875. So I can see a snippet of your paper that says round to the nearest tenth. Yay.
that would be 11.2. :>
The height is 11.2!! So now... oh noes you have to do it again.
Except this time, you're solving for a^2!
Switch the formula like this: c^2 - b^2 = a^2
13^2 - 11.2^2 = a^2 (base)
43.56 = a^2
6.6 = a
So now, the base is 6.6 + 10, which is 16.6 in total. 13 and 15 are the two side lengths. But you don't need those. You only need the height, 11.2. So multiply 16.6 x 11.2, and you get 185.92, or 185.9. Then divide that by two, since it's a triangle, not a square. That's 92.96. Yay you have the area!
Hypotenuse formula: a^2 + b^2 = c^2
Use this if you don't have the given height, so you can solve for it. The dashed line separated the triangle into two parts, so you could find the needed sides of both triangles. Later, when you get into triangle proofs, you could use the "by construction" postulate to be able to find the similarity or congruence done here.
Have a good day!