Common Geometric Shapes Quiz

Common Geometric Shapes

1. Polygon

• A closed figure with straight sides.
• Examples: Triangle, Quadrilateral, Pentagon, Hexagon, etc.

2. Triangle

• A three-sided polygon.
• Types:
  • Equilateral: All sides equal.
  • Isosceles: Two sides equal.
  • Scalene: All sides different.
• Sum of interior angles: 180°.

3. Quadrilateral

• A four-sided polygon.
• Types:
  • Square: All sides equal, angles 90°.
  • Rectangle: Opposite sides equal, angles 90°.
  • Parallelogram: Opposite sides equal, angles not 90°.
  • Trapezoid: At least one pair of parallel sides.
• Sum of interior angles: 360°.

4. Circle

• A round shape with all points equidistant from the center.
• Key properties:
  • Diameter: Distance across the circle through the center.
  • Radius: Distance from the center to any point on the circle.
  • Circumference: 2πr (where r is the radius).

5. Ellipse

• An elongated circle, defined by two focal points.
• Key properties:
  • Major axis: Longest diameter.
  • Minor axis: Shortest diameter.

6. 3D Shapes

• Cube:

  • Six equal square faces.
  • 12 edges, 8 vertices.

• Sphere:

  • A perfectly round 3D shape.
  • All points equidistant from the center.

• Cylinder:

  • Two parallel circular bases connected by a curved surface.

• Cone:

  • A circular base tapering smoothly to a point (the apex).

• Pyramid:

  • A base that is a polygon and triangular faces that converge at a point.

7. Symmetry

• A shape is symmetric if it can be divided into parts that are mirror images.
• Types:
  • Reflective symmetry: Mirror image across a line.
  • Rotational symmetry: Shape looks the same when rotated.

8. Area and Perimeter

• Area: The space contained within a shape.
• Perimeter: The total distance around a shape.

Key Formulas

• Triangle: Area = 1/2 × base × height
• Rectangle: Area = length × width; Perimeter = 2(length + width)
• Circle: Area = πr²; Circumference = 2πr
• Square: Area = side²; Perimeter = 4 × side

Polygon

• Defined as a closed figure composed of straight sides.
• Common examples include Triangle, Quadrilateral, Pentagon, and Hexagon.

Triangle

• A polygon characterized by three sides.
• Types include:
  • Equilateral: All sides and angles are equal.
  • Isosceles: Two sides are equal in length.
  • Scalene: All sides are of different lengths.
• Interior angles always sum up to 180°.

Quadrilateral

• A polygon with four sides.
• Types include:
  • Square: All sides are equal, and each angle measures 90°.
  • Rectangle: Opposite sides are equal, each angle is 90°.
  • Parallelogram: Opposite sides are equal but angles are not restricted.
  • Trapezoid: At least one pair of parallel sides.
• Interior angles sum up to 360°.

Circle

• A round shape where all points are equidistant from a center point.
• Key properties include:
  • Diameter: The distance across the circle through the center.
  • Radius: The distance from the center to any point on the circle.
  • Circumference formula: 2πr, with r being the radius.

Ellipse

• An elongated circular shape, characterized by two focal points.
• Key measurements include:
  • Major axis: The longest diameter of the ellipse.
  • Minor axis: The shortest diameter.

3D Shapes

• Cube:
  • Comprised of six equal square faces, 12 edges, and 8 vertices.
• Sphere:
  • A three-dimensional round shape with all points equidistant from the center.
• Cylinder:
  • Features two parallel circular bases connected by a curved surface.
• Cone:
  • Has a circular base that tapers smoothly to a single point known as the apex.
• Pyramid:
  • Characterized by a polygonal base and triangular faces converging at a single point.

Symmetry

• A shape exhibits symmetry if it can be divided into mirror image parts.
• Types include:
  • Reflective symmetry: Divided across a line producing mirror images.
  • Rotational symmetry: Remains unchanged when rotated around a center point.

Area and Perimeter

• Area refers to the space contained within a shape.
• Perimeter denotes the total distance around the edge of a shape.

Key Formulas

• Triangle: Area = 1/2 × base × height.
• Rectangle: Area = length × width; Perimeter = 2(length + width).
• Circle: Area = πr²; Circumference = 2πr.
• Square: Area = side²; Perimeter = 4 × side.