## Irregular Shape Areas - Sample Math Practice Problems

The math problems below can be generated by MathScore.com, a math practice program for schools and individual families. References to complexity and mode refer to the overall difficulty of the problems as they appear in the main program. In the main program, all problems are automatically graded and the difficulty adapts dynamically based on performance. Answers to these sample questions appear at the bottom of the page. This page does not grade your responses.

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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:

### 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:

### 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:

### 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:
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
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

### 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:
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
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

### 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:
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
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