Question

Find the area.

Answer 1

C.) 294 square units.

First you use the pythagrian theorem, which is
$a {}^{2} + b {}^{2} = c {}^{2}$
C being the hypotenuse.

So plugging in the values of the triangle should look like this:
$a {}^{2} + 21 {}^{2} = 35 {}^{2}$
You need to get a alone, so you take the 35^2 which is 1225 and subtract the 21^2, which is 441 from 1225. You should get 784 and by taking the square root of that, you should get 28, which is the value of side a.

Then you need to use the area of a triangle formula which is base times height times (1/2), or bh(1/2)=A. The base is 28 and the height is 21, so multiply those to get 588. Divide by 2 and you get 294, the answer.

Hope this helps :)