The first one, 62.4. To find the area, you need to know all lengths of the sides of the triangle. To find the side shared with the square, which is adjacent to the angle 30 degrees, use cosine. cos30 = x over 8, the hypotenuse. The cosine of 30 is .866025404, so multiply that to the hypotenuse, 8. You get 6.92820323. To find the other side, you can do Pythagorean Theorem, or Trigonometry. Pythagorean Theorem is a squared plus 6.92820323 squared equals 8 squared. 6.92820323 squared is 48, subtracted by 8 squared, or 64, equals 16. A squared + 48 = 64. 16 square rooted is 4. So, the sides are 48 square rooted and 4. To find the area of the square, take the square root of 48 and multiply 7. Add that number, 48.49742261, to 1/2(6.92820323 x 4), which equals 62.4, approximately.
