Area Of Squares, Rectangles, Triangles, Parallelograms and Trapezoids

🔑 Key Concepts

  • Area measures the amount of two-dimensional space inside a figure.
  • Rectangles and squares use length multiplied by width.
  • Parallelograms use a base and its corresponding perpendicular height.
  • Triangles have half the area of a parallelogram with the same base and height.
  • Trapezoids use the average of the two parallel bases multiplied by the height.
  • Area is always expressed in square units.

✏️ Worked Examples - Area of Various 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 inches, square feet, or square centimeters.

💡 Main Idea

This lesson reviews how to select and apply area formulas for rectangles, squares, triangles, parallelograms, and trapezoids. Although the formulas differ, each one depends on identifying the correct dimensions. The height used in a formula must be perpendicular to the selected base. Diagrams, grids, and decomposition can help make these relationships easier to see.

📚 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 and fractions, dividing by \(2\), identifying parallel and perpendicular lines, and reading dimensions from diagrams or coordinate grids.

🚀 What Comes Next

These area formulas can next be applied to composite figures, shaded regions, figures with missing dimensions, and shapes drawn on coordinate grids. Area skills also support future work with circles, surface area, volume, and real-world measurement problems.

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