Use a ruler to measure each side of a shape. Shapes are defined by their length and number of sides; thus, after measuring, you will be able to determine the shape. For example, if you have a shape with four sides that are all equivalent, you know it is a square. A triangle has three sides, etc.
Find the exact length, width, height or radius of the shape by carefully tracing a line along the shape with a pencil and ruler and reading the measurement. You will need the exact number in order to determine the angles and area of the shape, which the protractor normally provides.
Determine the shape that you are measuring and find the equations that are used for that shape. For example, the area of a triangle is 1/2 the base times the vertical height (area = 1/2b --- h) and the total degrees equal 180.
Calculate the area using the formula for the specific shape. For a triangle, if the height is 4 inches and the base is 6 inches, the area is 12 inches (12 = 1/2(6) x 4).
Use trigonometry to solve for an angle in the triangle when you do not have any angles. In the example above, a right angle is formed by cutting the triangle in half so that the smaller triangle has a height of 4 inches a base of 3 inches. Use the Pythagorean theorem to solve for the hypotenuse.
a^2 + b^2 = c^2
4^2 + 3^2 = c^2 --> 16 + 9 = c^2 --> 25 = c^2 --> 5 = c
Use the sine function next, which is height divided by the hypotenuse or 4/5. Enter the function into a calculator to find sin(4/5) = 71 degrees. You now know two angles in the triangle, with the right angle equal to 90 degrees. The remaining angle in the half triangle is:
180 = 71 + 90 + x = 19
For the full triangle, double the angle you just found and solve for the remaining angle.
71 + (19 X 2) + y = 180 --> y = 71
The three angles are 71 degrees, 71 degrees and 38 degrees.