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Grade 8 · Spatial Sense · Composite Measurement and the Pythagorean Theorem

Measure Composite Spaces

Composite measurement combines familiar parts. The Pythagorean theorem uses the areas of squares on a right triangle's sides to find an unknown length.

The big idea

Decomposition turns unfamiliar measurements into known ones

For a right triangle, a² + b² = c². For composite areas, surfaces, and volumes, identify non-overlapping familiar pieces and combine their measures.

Work it through

Find the hypotenuse when legs are 6 cm and 8 cm

  1. 1. Identify c as the hypotenuse opposite the right angle.
  2. 2. Substitute: 6² + 8² = c².
  3. 3. Calculate: 36 + 64 = 100, so c² = 100.
  4. 4. Take the positive square root: c = 10 cm.