Geometry

11.3Areas 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, h.

b1

b2

h hh

Area of a Trapezoid

The area of a trapezoid equals half the product of height and the sum of the bases.

A = ½h(b1+ b2)

Area = ½(6)(8 + 12) = 60 square units

b1

h

b2

8

12

6

A = mhor

m is the median,the average ofthe bases

Area = 10(6) = 60 square units

Exercises

103

7

8

11

18 15

12

3060

4510

8 2

1. A = ½(11)(18+8)

A = 143

2. A = ½(10)(7+3)

A = 50

3. A = ½(6√3)(30+15)

A = 135√3

30º

6√3

6

4. A = ½(8)(10+2)

A = 48

8

8 2

2

Try # 2 and #4!

Easy method : Find m first

A = ½h(b1+ b2)m is the median length of the trapezoid

m = ½ (b1+ b2)

So, more simply:

A = h•mIt is the average of the bases

Exercises

5. m = ½(15 + 13) m = 14 A = 5(14) = 70

6. m = ½(25 + 10) m = 17.5 140 = 17.5 h h = 8

7. 46 = 4m m = 11.511.5 = ½(8 + b2)23 = 8 + b2

b2 = 158. 7 = ½(b1 + 9) 14 = b1 + 9 b1 = 5

6 3

33 3

5. 6. 7. 8. 9. 10.

b1 15 25 8 14x

b2 13 10 9 8

h 5 4 5 7x

A 140 46 70x2

m 7

= h•m

edian

70

14

8

17.5 11.5

15

5

35

3

5.5

6x

10x9. 6√3m = 33√3 m = 5.5 5.5 = ½(b1 + 8) 11 = b1 + 8 b1 = 3

10. 70x² = 7x • m m = 10x b1 = 6x

Exercises

Find the area of each isosceles trapezoid.

12 12

12

2460 60

10

30

2626

1010

x

x² + 10² = 26²

x² + 100 = 676

x² = 576x = √576x = 24

m = ½(30+ 10)

m = 20

A = 24 • 20

A = 480

6

6√3

m = ½(24 + 12)

m = 18

A = 6√3 • 18

A = 108√3

5-12-13 Triple

Exercises

Find the area of an isosceles trapezoid with legs 25 cm and bases 16 cm and 30 cm.

13.

25 25

16

30 7 30 - 162

7-24-25 Triple

24

m = ½(16 + 30)

m = 23 A = 24 • 23 = 552 552 cm²

7

Exercises

Find the area of a trapezoid with 45˚ base angles and bases 17 and 23.

14.

3√2

17

23 3 23 - 172

45-45-90 Rt. ∆

3

m = ½(17 + 23)

m = 20 A = 3 • 20 = 60 60 sq. units

45 45

3

Homework

pg. 436 #1-19, 23 odd pg. 470 #1-9 For #5 see the bonus from Powerpoint 11.2