Geometry in Real World: Painting Walls

Determining Area in Real-World Scenarios

• Real-world scenarios often involve complex shapes, requiring application of area formulas to determine surface area.

Review of Basic Shapes

• Rectangle: four-sided shape with 90-degree angles, opposite sides of equal length, area = width × height.
• Square: special type of rectangle with all sides of equal length, area = s^2, where s is the length of one side.
• Triangle: area = 1/2 × base × height, can use Pythagorean theorem (a^2 + b^2 = c^2) to find missing side.
• Circle: area = π × r^2, where r is the radius.

Complex Shapes

• Divide complex shapes into basic shapes (e.g., rectangles, triangles) to calculate area.
• Examples:
  • Wall with angled ceiling: divide into two rectangles, calculate area of each.
  • Room with corner: divide into rectangle and right triangle, calculate area of each.

Parts of Shapes

• To find area of wall space, subtract area of obstacles (e.g., doors, windows) from total area of wall.
• Examples:
  • Wall with one door: subtract door's area (7 × 3 = 21 square feet) from wall's area (8 × 12 = 96 square feet).
  • Wall with two windows and dog door: subtract total area of windows and dog door (18 + 1.5 = 19.5 square feet) from wall's area (11 × 8 = 88 square feet).

Real-World Applications

• Pizza box: calculate empty surface space by subtracting pizza's area (π × r^2, where r is 6 inches) from box's area (13^2 = 169 square inches).
• Painting walls: calculate area of wall space to determine amount of paint needed.