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Area of a Trapezoid

Part of the Polygons & Quadrilaterals section of Coddy's Geometry journey. Lesson 42 of 61.

Put two copies of a trapezoid together, one turned upside down. They make a parallelogram whose base is the two parallel sides end to end, a + b, with the same height h. That parallelogram has area (a + b) × h, so one trapezoid is half of it.

$Trapezoid with parallel sides 10 and 6 and height 4$

So area of a trapezoid = ½ × (a + b) × h. Here the parallel sides are 10 and 6 and the height is 4: 1/2 × (10 + 6) × 4 = 32. The height is the distance between the parallel sides, at right angles to them.

Challenge

ABCD is a trapezoid with AB ∥ DC, AB = 12, DC = 6 and the dashed height DE = 5. Find its area, then press Check.

Try it yourself

$Find the marked part of the figure$

Find the marked part of the figure

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

All lessons in Polygons & Quadrilaterals

2Regular Polygons

Regular Polygons From an Angle to the Sides Inside a Regular Polygon Recap: Regular Polygons

5Rectangles, Rhombi, Squares

Rectangles The Diagonal of a Rectangle Rhombus Angles Squares Recap: Special Parallelograms

8Area of Parallelograms

Area of a Rectangle A Side from the Area Slide the Top Area of a Parallelogram Recap: Parallelogram Area

11Polygon Chases

Parallel Sides in a Pentagon Marks, Not Looks Pentagon with x Regular Shapes Together Recap: Polygon Chases

3Exterior Angles

Exterior Angles Exterior Angles Make 360°Regular Exterior Angles Sides from the Exterior Recap: Exterior Angles

6Trapezoids and Kites

Trapezoids Isosceles Trapezoids Trapezoids with x Kites Recap: Trapezoids and Kites

9Area of Trapezoids

Area of a TrapezoidA Missing Base Find the Height First Trapezoids by Area Recap: Trapezoid Area

12Final Challenges

Final: The Garden Bed Final: Enough to Finish?Final: The Ramp Final: The Gable Wall Final: The Star Point