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 figure inside is a square. Area:

2.   The triangle inside is equilateral. Area:

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 a right triangle. Area:

2.   The triangle inside is equilateral. Area:

Complexity=3

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

1.   The figure inside is a square. Area:

2.   The figure inside is a square. Area:

Answers

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 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

#	Problem	Correct Answer	Your Answer
2	The triangle inside is equilateral.	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

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 a right triangle.	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 = 42 + 52 = 16 + 25 = 41 Area of circle = πr2 = πd2 /4 = 3.14 × 41/4 = 32.185 Area of triangle = bh/2 = 4 × 5 / 2 = 10 Area = Area of Circle - Area of triangle = 32.185 - 10 = 22.19

#	Problem	Correct Answer	Your Answer
2	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

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 inside is a square.	Area:
Solution Area = Area(Circle) - Area(Square) Diagonal of square = 1 Side of square = Diagonal/(√2) Area of square = s2 = Diagonal2 /2 = 12/2 = 0.5 Area of circle = πr2 = πd 2/4 = 3.14 × 12/4 = 0.785 Area = Area of circle - Area of square = 0.785 - 0.5 = 0.29

#	Problem	Correct Answer	Your Answer
2	The figure inside is a square.	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