ACT Preparation / Unit 14 ACT 1305 worked example, 60 to 90 seconds
Area of a Shaded Region
The idea
A shaded-region area is found in three steps. First, identify the outer shape and the shape or shapes removed from it. Second, compute each area separately, finding any missing dimension from the figure: a circle that fits exactly inside a square has a diameter equal to the square's side. Third, subtract the removed areas from the outer area, and leave the answer in terms of π unless a decimal is asked for.
In practice
Worked example: a circle fits exactly inside a square of side 8. The shaded corners are the square minus the circle. Square: 8² = 64. The circle's diameter is 8, so its radius is 4 and its area is 16π. Shaded area: 64 − 16π, about 13.7 square units.
Where people slip
Check which region is shaded before subtracting. Here the corners lie outside the circle; if the circle itself were shaded, the answer would be 16π.
Your place on the trail
Every lesson rests on earlier ones and opens later ones. Tap any to jump.
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