June 15, 2021 3:55 pm
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June 15, 2021 3:55 pm
Topic starter
You do not need to draw any new line segments for this question. The perimeter of the shaded region is BC + AB + AE + arc EC. The quarter circle has its center at D, and point C lies on the circle, so side DC is a radius of the quarter circle and has length 4. Opposite sides of a rectangle are equal, so AB = 4 also. The perimeter of the rectangle is 20, so BC and AD are each 6. Because AD=6 and ED=4, you know that AE=2. The circumference of a full circle with radius is
so the length of a quarter circle arc is
Arc EC is a quarter circle arc of a circle with radius 4, so its length is
So the perimeter of the shaded region is