Area Of Trapezoids

🔑 Key Concepts

  • The parallel sides of a trapezoid are called its bases.
  • The height is the perpendicular distance between the two bases.
  • The area formula is \(\displaystyle A=\frac{1}{2}(b_1+b_2)h\).
  • Adding the bases and dividing by \(2\) finds their average length.
  • The average base length can be viewed as the width of an equivalent rectangle with the same height and area.
  • A slanted side is not the height unless it is perpendicular to both bases.

✏️ Worked Examples - Finding the Area of Trapezoids

🧠 Math Vocabulary

  • Trapezoid: A quadrilateral with at least one pair of parallel sides.
  • Bases: The parallel sides of a trapezoid.
  • Height: The perpendicular distance between the two bases.
  • Perpendicular: Intersecting at a right angle of \(90^\circ\).
  • Average: A value found by adding quantities and dividing by the number of quantities.
  • Equivalent figures: Figures that may have different shapes but have the same area.
  • Right trapezoid: A trapezoid containing two right angles.
  • Isosceles trapezoid: A trapezoid whose nonparallel sides are congruent.
  • Square unit: A unit used to measure area, such as square inches or square centimeters.

💡 Main Idea

The area of a trapezoid can be understood as the area of a rectangle whose width is the average of the trapezoid’s two parallel bases. Adding \(b_1\) and \(b_2\) and dividing by \(2\) finds that average base length. Multiplying the average base by the perpendicular height gives \(\displaystyle A=\frac{1}{2}(b_1+b_2)h\).

📚 What You Should Already Know

You should understand that area measures the space inside a two-dimensional figure in square units. You should also be able to identify parallel and perpendicular lines, calculate an average by adding and dividing, and multiply whole numbers or decimals.

🚀 What Comes Next

Next, you can find trapezoid areas with decimal or fractional dimensions, determine missing measurements from a known area, and use trapezoids as parts of composite figures. These skills also support future work with surface area, coordinate geometry, and volume.

🧩 Embed This Video in Your LMS

Teachers can embed this YouTube video directly into Canvas, Google Classroom, Schoology, or another learning platform. Click below to show the embed code.