1. Geometry
11.3
Areas of Trapezoids

2. 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 h h h b2

3. A = ½h(b1+ b2) A = mh Area of a Trapezoid
The area of a trapezoid equals half the product of height and the sum of the bases. b1 8
A = ½h(b1+ b2) 6 h or 12
A = mh b2
m is the median,
the average of
the bases
Area = ½(6)(8 + 12) = 60 square units
Area = 10(6) = 60 square units

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

5. Easy method : Find m first
A = ½h(b1+ b2)
m is the median length of the trapezoid
m = ½
(b1+ b2)
So, more simply:
It is the average of the bases
A = h•m

6. Exercises 5 3 15 6x 8 70 35 14 17.5 11.5 5.5 10x = h•m edian6. 7. 8. 9.
10. b1 15 25 8
14x b2 13 10 9 h 5 4 7x A
140 46
70x2 m 7 5 3 15 6x 8
= h•m 70 35
edian 14
17.5
11.5
5.5
10x
= 4m
m = 11.5
11.5 = ½(8 + b2)
23 = 8 + b2
b2 = 15
9. 6√3m = 33√3
m = 5.5
5.5 = ½(b1 + 8)
11 = b1 + 8
b1 = 3
5. m = ½( )
m = 14
A = 5(14) = 70
6. m = ½( )
m = 17.5
140 = 17.5 h
h = 8
8. 7 = ½(b1 + 9)
14 = b1 + 9
b1 = 5
10. 70x² = 7x • m
m = 10x
b1 = 6x

7. Exercises Find the area of each isosceles trapezoid. 5-12-13 Triple x6 12 24
60 10 30 26
6√3 x 10 10
m = ½( )
x² + 10² = 26²
m = ½(30+ 10)
m = 18
x² = 676
m = 20
x² = 576
A = 6√3 • 18
A = 24 • 20
x = √576
A = 108√3
A = 480
x = 24

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

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

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