Quickly Find The Area of a Trapezoid

🔑 Key Concepts

  • The parallel sides of a trapezoid are its bases.
  • The height is the perpendicular distance between the bases.
  • Add the bases and divide by \(2\) to find their average length.
  • Multiply the average base by the height.
  • This is equivalent to \(\displaystyle A=\frac{1}{2}(b_1+b_2)h\).

💡 Main Idea

To find the area of a trapezoid, average the lengths of the two parallel bases and multiply that average by the perpendicular height. In other words, add the bases, divide by \(2\), and multiply by the height. This process works for right trapezoids, isosceles trapezoids, and trapezoids with two different slanted sides.

✏️ Worked Examples

🧠 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.
  • Average: A value found by adding quantities and dividing by the number of quantities.
  • Right trapezoid: A trapezoid containing two right angles.
  • Isosceles trapezoid: A trapezoid whose nonparallel sides are congruent.
  • Scalene trapezoid: A trapezoid whose nonparallel sides have different lengths.
  • Perpendicular: Forming a right angle of \(90^\circ\).
  • Square unit: A unit used to measure area.

📚 What You Should Already Know

You should understand area as the amount of space inside a two-dimensional figure and know how to identify parallel and perpendicular lines. You should also be comfortable adding, dividing by \(2\), multiplying, and distinguishing a perpendicular height from a slanted side.

🚀 What Comes Next

Next, students can find trapezoid areas with decimal or fractional dimensions, determine missing bases or heights, and use trapezoids as parts of composite figures and shaded regions.

🧩 Embed This Video in Your LMS

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