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A Missing Base

Part of the Polygons & Quadrilaterals section of Coddy's Geometry journey. Lesson 41 of 59.

With the area given, the trapezoid rule becomes an equation for a missing length. A parallel side is the usual unknown.

$Trapezoid with area 30, parallel sides 9 and x, height 4$

Here $30 = \frac{1}{2}\cdot \left(9+x\right)\cdot 4$ . Half of 4 is 2, so $30 = 2\cdot \left(9+x\right)$ . Divide by 2: $15 = 9+x$ , and $x = 6$ . Check it: ½ × (9 + 6) × 4 = 30.

Challenge

ABCD is a trapezoid with area 36, AB = 8, DC = x and the dashed height DE = 4. Tap the parts, pick the rule, and solve the equation the board writes for x.

Then press Check.

Try it yourself

$Use the figure to find x$

Use the figure to find x

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 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 BaseFind 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