Irregular Shape Areas - Sample Math Practice Problems

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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.   The triangle inside is equilateral. Area:

2.   The figure outside is a square. 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.   The triangle inside is equilateral. Area:

2.   The figure outside is a square. 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.   The figure outside is a square. Area:

2.   The figure inside is a square. 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	The triangle inside is equilateral.	Area:
Solution Area = Area(circle) - Area(Triangle) Area(circle) = πr2 = 3.14 × 52 = 78.5 Side length of triangle = √3 × radius = √3 × 5 = 8.66 Area of equilateral triangle = √(3)s2 /4 = √(3) × 8.662/4 = 32.48 Area = Area of circle - Area of triangle = 78.5 - 32.48 = 46.02

#	Problem	Correct Answer	Your Answer
2	The figure outside is a square.	Area:
Solution Area = Area(Square) - Area(Circle) Side length of square = Diameter = 3 Area of circle = πr2 = πd2/4 = 3.14 × 32/4 = 7.065 Area of square = s2 = 32 = 9 Area = Area(square) - Area(circle) = 9 - 7.065 = 1.94

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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	The triangle inside is equilateral.	Area:
Solution Area = Area(circle) - Area(Triangle) Area(circle) = πr2 = 3.14 × 42 = 50.24 Side length of triangle = √3 × radius = √3 × 4 = 6.93 Area of equilateral triangle = √(3)s2 /4 = √(3) × 6.932/4 = 20.78 Area = Area of circle - Area of triangle = 50.24 - 20.78 = 29.46

#	Problem	Correct Answer	Your Answer
2	The figure outside is a square.	Area:
Solution Area = Area(Square) - Area(Circle) Diameter of circle = 2 × 9 = 18 Side length of square = Diameter = 18 Area of circle = πr2 = 3.14 × 92 = 254.34 Area of square = s2 = 182 = 324 Area = Area(square) - Area(circle) = 324 - 254.34 = 69.66

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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	The figure outside is a square.	Area:
Solution Area = Area(Square) - Area(Circle) Diameter of circle = 2 × 10 = 20 Side length of square = Diameter = 20 Area of circle = πr2 = 3.14 × 102 = 314 Area of square = s2 = 202 = 400 Area = Area(square) - Area(circle) = 400 - 314 = 86

#	Problem	Correct Answer	Your Answer
2	The figure inside is a square.	Area:
Solution Area = Area(Circle) - Area(Square) Diagonal of square = 2 × 8 =16 Side of square = Diagonal/(√2) Area of square = s2 = Diagonal2 /2 = 162/2 = 128 Area of circle = πr2 = 3.14 × 82 = 200.96 Area = Area of circle - Area of square = 200.96 - 128 = 72.96