Area Of Rectangles, Squares, Parallelograms, Trapezoids And Triangles

🔑 Key Concepts

  • Area measures the amount of two-dimensional space inside a figure.
  • Rectangles, squares, and parallelograms use a base multiplied by a perpendicular height.
  • A triangle has half the area of a parallelogram with the same base and height.
  • A trapezoid’s area uses the average of its two parallel bases multiplied by its height.
  • The height must always be perpendicular to the selected base.
  • Area is measured in square units.

✏️ Worked Examples - Area of Different Polygons

🧠 Math Vocabulary

  • Area: The amount of two-dimensional space inside a figure, measured in square units.
  • Base: A selected side of a figure used with its corresponding perpendicular height.
  • Perpendicular height: The shortest distance from a base to the opposite side or vertex, measured at a right angle.
  • Rectangle: A quadrilateral with four right angles.
  • Square: A rectangle with four congruent sides.
  • Parallelogram: A quadrilateral with two pairs of parallel opposite sides.
  • Trapezoid: A quadrilateral with at least one pair of parallel sides.
  • Triangle: A polygon with three sides and three angles.
  • Square unit: A unit used to measure area, such as square centimeters or square inches.

💡 Main Idea

Different figures use different area formulas, but each formula depends on dimensions that describe the space inside the shape. Rectangles, squares, and parallelograms use a base multiplied by a matching perpendicular height. Triangles use half that product, while trapezoids use the average of their two parallel bases multiplied by the height. Correctly identifying the base and perpendicular height is essential.

📚 What You Should Already Know

You should understand that area measures the interior of a two-dimensional figure in square units. You should be comfortable multiplying whole numbers, dividing by \(2\), recognizing parallel and perpendicular lines, and distinguishing a perpendicular height from a slanted side.

🚀 What Comes Next

These area formulas can next be applied to figures with fractional or decimal dimensions, shapes drawn on coordinate grids, and composite figures made from several basic shapes. Area skills also support future work with circles, surface area, and volume.

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