Area and Perimeter: Trapezoids Keystone Geometry

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

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.

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

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

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

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) =

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

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