Geometry 11 3 Areas of Trapezoids Trapezoids In

Geometry 11. 3 Areas of Trapezoids

Trapezoids In a trapezoid, the bases are the parallel sides. An altitude of a trapezoid is defined in the same way as an altitude of a parallelogram. The altitude of a trapezoid is any segment perpendicular to a line containing one base from a point on the opposite base. In a trapezoid, all altitudes have the same length, called the height, b 1 h h b 2 h h.

Area of a Trapezoid The area of a trapezoid equals half the product of height and the sum of the bases. b 1 8 6 h b 2 12 A = ½h(b 1+ b 2) or A = mh m is the median, the average of the bases Area = ½(6)(8 + 12) = 60 square units Area = 10(6) = 60 square units

Exercises Try # 2 and #4! 30º 18 11 7 10 3 12 60 6 8 1. A = ½(11)(18+8) A = 143 8 15 45 6√ 3 2 10 30 8 2 3. A = ½(6√ 3)(30+15) A = 135√ 3 2. A = ½(10)(7+3) A = 50 4. A = ½(8)(10+2) A = 48

Easy method : Find m first m is the median length of the trapezoid A = ½h(b 1+ b 2) m = ½(b 1+ b 2) It is the average of the bases So, more simply: A = h • m

Exercises 5. 6. 7. 8. 9. 10. b 1 15 25 8 5 3 14 x b 2 13 10 15 9 8 6 x h 5 8 4 5 7 x 70 140 46 35 70 x 2 A = h • m m edian 5. 14 m = ½(15 + 13) m = 14 A = 5(14) = 70 6. m = ½(25 + 10) m = 17. 5 140 = 17. 5 h h = 8 17. 5 11. 5 7. 46 = 4 m m = 11. 5 = ½(8 + b 2) 23 = 8 + b 2 = 15 8. 7 = ½(b 1 + 9) 14 = b 1 + 9 b 1 = 5 7 5. 5 9. 6√ 3 m = 33√ 3 m = 5. 5 = ½(b 1 + 8) 11 = b 1 + 8 b 1 = 3 10 x 10. 70 x² = 7 x • m m = 10 x b 1 = 6 x

Exercises Find the area of each isosceles trapezoid. 5 -12 -13 Triple 10 26 10 x 30 26 6 60 12 24 60 6√ 3 12 12 10 x² + 10² = 26² m = ½(30+ 10) x² + 100 = 676 m = 20 x² = 576 A = 24 • 20 x = √ 576 A = 480 x = 24 m = ½(24 + 12) m = 18 A = 6√ 3 • 18 A = 108√ 3

Exercises 13. Find the area of an isosceles trapezoid with legs 25 cm and bases 16 cm and 30 cm. 16 25 7 -24 -25 Triple 25 24 7 30 - 16 2 m = ½(16 + 30) m = 23 A = 24 • 23 = 552 cm²

Exercises 14. Find the area of a trapezoid with 45˚ base angles and bases 17 and 23. 45 -45 -90 Rt. ∆ 17 3√ 2 3 45 23 3 23 - 17 2 m = ½(17 + 23) m = 20 A = 3 • 20 = 60 60 sq. units

Homework pg. 436 #1 -19, 23 odd pg. 470 #1 -9 For #5 see the bonus from Powerpoint 11. 2