1. Area and Perimeter: Trapezoids Keystone Geometry

2. Trapezoid Median Theorem
Review of Trapezoids
The || sides are bases;
the other sides are legs. 1 2 3 4
Base angles:
& b1 C A B N M D m b2
Trapezoid Median Theorem

3. Altitude & Height of a Trapezoid
Def: An altitude of a trapezoid is any segment perpendicular to a line containing a base from a point on the opposite base. C A B D E F
are altitudes
Def: The height of a trapezoid is the length of an altitude.

4. Area of a Trapezoid b1 b2 h
Area of a Trapezoid: The area of a trapezoid is one half the product of the height & the sum of the bases.
Since

5. Examples
1. Find (a) the area of the trapezoid & (b) the length of its median. 7 6 10 13

6. Examples 5 6 10
2. Find the area of an isosceles trapezoid with legs 5 & bases 6 & 10. h 2 6
by Pyth. Thm

7. Summary h s h h b b b h b1 h h b b2 A(square) = s2=bh
A(rectangle) = bh
A(||-gram) = bh h b h b1 h b b2
A(triangle) =
A(rhombus) = bh
A(trapezoid) =

8. Practice Examples 1. 2. 6 3. 10 15 6 6
60
60 5 18 10 8 4. 5. 6. 2
45
60
60 8 3 3 6
30 3 10

9. Practice Examples (with Trigonometry)7. 7 8. 9. 8 6 10 10 6
35
38
40 13