1.16.7.a. Computation of areas

Try these first

1. 1.

   What is the Trapezoidal Rule used for?

   Hint

   Think of dividing shapes into simpler parts.

2. 2.

   What is a planimeter?

   Hint

   Consider a tool that 'walks' around a shape.

3. 3.

   What does the Trapezoidal Rule approximate?

   • Area under a curve
   • Volume
   • Length

   Hint

   Think about shapes that have parallel sides.

4. 4.

   Simpson's Rule uses what to estimate area?

   • Parabolic arcs
   • Straight lines

   Hint

   Visualize how curves fit within lines.

5. 5.

   A plot measures 12 meters on one side, 14 meters on another, and the remaining two sides create a trapezoidal section with heights of 5 meters each. Calculate the area using the trapezoidal rule.

   Hint

   Remember to average the lengths of the bases.

6. 6.

   Using coordinates, calculate the area of a polygon with vertices at (2,3), (5,11), (12,8), and (10,5).

   Hint

   Use the coordinate formula carefully.