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Find the Height First

Part of the Polygons & Quadrilaterals section of Coddy's Geometry journey. Lesson 44 of 61.

Often the height is not given, but a slanted leg is. Drop the height from the end of the leg: it makes a right triangle whose hypotenuse is the leg. The Pythagorean theorem then gives the height.

$Trapezoid with leg 13, the foot of the height 5 from A, and height h$

Here the leg AD is 13 and E is 5 from A, so h^2 + 5^2 = 13^2, which gives h^2 = 144 and h = 12. Only then does the area rule have all it needs: ½ × (16 + 6) × 12 = 132. Two rules in a row: Pythagorean theorem, then Area of a trapezoid.

Challenge

ABCD is a trapezoid with AB ∥ DC, AB = 11, DC = 5 and the leg AD = 5. The dashed height DE meets AB at E, 3 from A. Find the area of ABCD, 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 Trapezoid A Missing BaseFind the Height FirstTrapezoids 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