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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


Complexity=1

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

Complexity=2

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

Complexity=3

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

Answers


Complexity=1

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

Complexity=2

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

Complexity=3

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