The primary topic of Chapter Seven is to find the areas of various polygons, circles, sectors and segments of circles, and combinations of these. The Pythagorean Theorem is formally stated, proved, and put to use. Two special right triangles are examined, and another Geometry in History segment is presented.

What you can expect to learn

After completing these activities you should be able to

  1. Define area.
  2. State and apply area postulates.
  3. Derive and apply formulas for the areas of triangles and special quadrilaterals.
  4. Apply the Area Addition Postulate to find the areas of other regions.
  5. Find missing lengths given the area and other lengths of geometric figures.
  6. Complete proofs of and apply the Pythagorean Theorem and its converse.
  7. Define and find Pythagorean triples.
  8. Derive and apply relationships in 45-45-90 and 30-60-90 triangles.
  9. Derive and apply a formula for the areas of regular polygons.
  10. Derive and apply formulas for the areas of circles and their sectors and segments.
Activity List