Smart Math guide · Geometry Smarts

Find Area by Decomposing Shapes

Break an irregular figure into rectangles, triangles, circles, or other familiar pieces.

All levelsWorked example includedSelf-check included
← Smart MathRelated calculators
The method

How to use it

  1. Draw dividing lines.
  2. Compute each simple area.
  3. Add pieces or subtract cutouts.
Worked example

See it in action

An L-shape can be a 10×8 rectangle minus a 4×3 cutout: 80−12=68 square units.

Check your thinking

How to verify it

Estimate against the full 80-square-unit rectangle.

Keep learning

More Geometry Smarts guides

Geometry Smarts

Use the Pythagorean Theorem

For a right triangle, the square of the hypotenuse equals the sum of the squares of the legs.

Read guide →
Geometry Smarts

Use Similar Triangles for Indirect Measurement

Similar triangles have equal corresponding angles and proportional corresponding sides.

Read guide →
Geometry Smarts

Estimate Circles Before Using π

Use π≈3.14 or π≈22/7 when suitable, but first judge whether radius or diameter is being used.

Read guide →
Geometry Smarts

Use Angle Sums as Constraints

Known angle totals can turn geometry into simple subtraction.

Read guide →
CalculatorWiser

Calculators, math tools, reference tables, games, guides and a growing math library.

All calculators · Math Blog
Latest from the Math BlogWho invented mathematics?Euclid: life, ideas, and mathematical legacyWhy zero changed mathematicsMaya mathematics and calendars
Policies & trustPrivacy PolicyCookie PolicyAdvertising & Affiliate DisclosureTerms of UseDisclaimerEditorial PolicyAccessibilityPrivacy Choices