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These sample problems below for Irregular Shape Areas were generated by the MathScore.com engine.

Sample Problems For Irregular Shape Areas

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Complexity=1

Find the area of the highlighted region. Gives answers to the nearest hundreth. Use 3.14 for pi

1.   Area:

2.   Area:

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Complexity=2

Find the area of the highlighted region. Gives answers to the nearest hundreth. Use 3.14 for pi

1.   Area:

2.   Area:

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Complexity=3

Find the area of the highlighted region. Gives answers to the nearest hundreth. Use 3.14 for pi

1.   Area:

2.   Area:

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Answers

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Complexity=1

Find the area of the highlighted region. Gives answers to the nearest hundreth. Use 3.14 for pi

#	Problem	Correct Answer	Your Answer
1		Area:
Solution Area = Area(circle) - Area(Triangle) Area(circle) = πr2 = 3.14 × 82 = 200.96 Side length of triangle = √3 × radius = √3 × 8 = 13.86 Area of equilateral triangle = √(3)s2 /4 = √(3) × 13.862/4 = 83.14 Area = Area of circle - Area of triangle = 200.96 - 83.14 = 117.82

#	Problem	Correct Answer	Your Answer
2		Area:
Solution Area = Area(Circle) - Area(Square) Diagonal of square = 2 × 4 =8 Side of square = Diagonal/(√2) Area of square = s2 = Diagonal2 /2 = 82/2 = 32 Area of circle = πr2 = 3.14 × 42 = 50.24 Area = Area of circle - Area of square = 50.24 - 32 = 18.24

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Complexity=2

Find the area of the highlighted region. Gives answers to the nearest hundreth. Use 3.14 for pi

#	Problem	Correct Answer	Your Answer
1		Area:
Solution Area = Area(Square) - Area(Circle) Diameter of circle = 2 × 5 = 10 Side length of square = Diameter = 10 Area of circle = πr2 = 3.14 × 52 = 78.5 Area of square = s2 = 102 = 100 Area = Area(square) - Area(circle) = 100 - 78.5 = 21.5

#	Problem	Correct Answer	Your Answer
2		Area:
Solution Area = Area(Circle) - Area(Square) Diagonal of square = 8 Side of square = Diagonal/(√2) Area of square = s2 = Diagonal2 /2 = 82/2 = 32 Area of circle = πr2 = πd 2/4 = 3.14 × 82/4 = 50.24 Area = Area of circle - Area of square = 50.24 - 32 = 18.24

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Complexity=3

Find the area of the highlighted region. Gives answers to the nearest hundreth. Use 3.14 for pi

#	Problem	Correct Answer	Your Answer
1		Area:
Solution Area = Area(Circle) - Area(Triangle) All triangles with the longest side as the diameter of a circle are right triangles. Diameter2 = Hypotenuse2 = (side 1)2 + (side 2)2 = 72 + 42 = 49 + 16 = 65 Area of circle = πr2 = πd2 /4 = 3.14 × 65/4 = 51.025 Area of triangle = bh/2 = 7 × 4 / 2 = 14 Area = Area of Circle - Area of triangle = 51.025 - 14 = 37.03

#	Problem	Correct Answer	Your Answer
2		Area:
Solution Area = Area(Circle) - Area(Square) Diagonal of square = 2 × 10 =20 Side of square = Diagonal/(√2) Area of square = s2 = Diagonal2 /2 = 202/2 = 200 Area of circle = πr2 = 3.14 × 102 = 314 Area = Area of circle - Area of square = 314 - 200 = 114

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