Area of Shaded Regions Worksheet
This worksheet focuses on calculating the area of shaded regions in various geometric figures, including squares, circles, and triangles, at a Grade 9 level.
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Area of Shaded Regions
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Read each question carefully and calculate the area of the shaded region. Show all your work.
1. A square has a side length of 10 cm. A circle is inscribed within the square. What is the area of the shaded region (the area of the square minus the area of the circle)? Use π ≈ 3.14.
2. Find the area of the shaded region, which is the area of the larger rectangle minus the area of the smaller rectangle. The larger rectangle has a length of 12 cm and a width of 8 cm. The smaller rectangle has a length of 6 cm and a width of 4 cm. Both rectangles share the same center.
3. A semi-circle is cut out from a rectangle. If the rectangle has dimensions 10 units by 8 units, and the semi-circle has a radius of 4 units (with its diameter along one of the 8-unit sides), the area of the shaded region is square units. (Use π ≈ 3.14)
4. A square with side length 's' has four quarter-circles cut from each corner, each with a radius of s/2. Which expression represents the area of the remaining shaded region?
s² - π(s/2)²
s² - 4π(s/2)²
s² - πs²
s² - (1/4)π(s/2)²
5. The area of a shaded region formed by a circle inscribed in an equilateral triangle can be found by subtracting the area of the circle from the area of the triangle.
True
False