This can be proven by using the Pythagorean theorem. Draw a circle and label the radius 4 cm. Then draw the diameters in to create a perpendicular intersection at the center. If you then label the points that make the diameter, you will see that when connected they create right isosceles triangles. a^2 + b^2 = c ^2, so 4 x 4 + 4 x 4 = c^2. 32 = c^2. Because you are going to be multiplying it by itself to calculate the area, you have you answer of 32 square centimeters. NO need to find the square root and them square it again!
