The figure shows the blueprint that a contractor uses to design ice-skating rinks. Which expression gives the area of the spectator section shaded in red?
Step One Calculate the area of both the skating area and the spectator area.
Area = L * W L = 4x W = 4x Area = 4x * 4x Area = 16x^2
Step Two. Find the radius of the semicircle. R = radius From the diagram R = The full length - the length given in the red shaded area. R = 4x - 2x R = 2x
Step Three Find the area of the semicircle. Area of a full circle = pi R^2 Area of a 1/2 circle = [tex] \frac{ \pi*{(2x)}^2}{2} [/tex] Area of a 1/2 circle = [tex] \frac{ \pi*4*x^2}{2} [/tex] Area of a 1/2 circle = [tex] \frac{ \pi*2*x^2}{ } [/tex] Notice that the 2 in the denominator cancels in part with the 4 in the numerator.
Step Four Find the area of the shaded area Area of the shaded Area = Whole Area - Area of the Semi Circle. Area of the shaded Area = 16x² - [tex] \frac{ \pi*2*x^2}{ } [/tex]
