What is the Area of the Basketball Backboard?
Finding areas, working with real dimensions
What areas are covered?
Mixed dimensions Triangles Trapezoids Curvelinear figure Approximation
The Backboard Shape
To find area, what do we need?
We Need the Dimensions
3 1/2 feet 18 in 24 in 6 feet 18 in 1 foot
9 in
Lets divide up the backboard into regions
What about this one?
C
D
A
B
Two trapezoids and a Rectangle
The Top
We need to model the curve. It’s not anything in particular. Circle? No Parabola? Maybe Ellipse? Maybe Multiple trapezoids??
Divide into Two Regions
D1
a
D2 b
A
B
C
Models
If an ellipse use the area formula
Area full ellipse ab
If a parabola, use the area formula
Area parabolic segment 4 ab 3
Discussion: Compare the area of the half ellipse with the parabolic segment.
Trapezoids
D 1
a
D2 b
Subdivide and measure C A B
Discussion. (a) Error, (b) How to improve accuracy by adding more trapezoids
Basketball Backboard Problem
Shows approximation is needed for even common things. Shows the importance of decomposition to simpler regions. Shows that not everything is straight lines and circles. Shows the need for careful analysis.
Anyone up for a basketball court?