Area of Trapezoids
Goal
Find the area of trapezoids.
Key Vocabulary
Trapezoid
Base of a trapezoid
Height of a trapezoid
Trapezoid
A trapezoid is a
quadrilateral with exactly
one pair of parallel sides.
Each of the parallel sides
is called a base.
The nonparallel sides are
called legs.
Height of the trapezoid is
the shortest distance
(perpendicular distance)
between the bases.
Area of Trapezoid
b1=base 1
h=height
What
What is
is the
the area
area of
of this
this trapezoid?
triangle?
b2=base 2
Area of Trapezoid
b1=base 1
h=height
What is the area of
this trapezoid?
b2=base 2
COPY THIS!
Area of Trapezoid
b1=base 1
h=height
What is the area of
this trapezoid?
b2=base 2
PASTE HERE!
Area of Trapezoid
b1=base 1
h=height
What is the area of
this trapezoid?
b2=base 2
FLIP VERTICALLY!
Area of Trapezoid
b1=base 1
h=height
What is the area of
this trapezoid?
b2=base 2
FLIP HORIZONTALLY!
Area of Trapezoid
b1=base 1
h=height
What is the area of
this trapezoid?
b2=base 2
TRANSLATE TO HERE!
Area of Trapezoid
b1=base 1
h=height
What is the area of
this trapezoid?
b2=base 2
b1=base 1
CHECK MEASUREMENTS!
Area of Trapezoid
b1=base 1
Area of the trapezoid is
½ the area of this
parallelogram?
b2=base 2
b1=base 1
h=height
Area of Trapezoid
b1=base 1
h=height
Areatrapezoid =
½ height(base 1 + base 2)
b2=base 2
b1=base 1
Area of Trapezoid
b1=base 1
h=height
Areatrapezoid = ½ h(b1 + b2)
b2=base 2
b1=base 1
Area of Trapezoid
Words:
Area = ½(height)(base1+base2)
Symbols:
A = 1/2h(b1+b2)
Example 1
Find the Area of a Trapezoid
Find the area of the trapezoid.
SOLUTION
1
A = h(b1 + b2)
2
1
= 2 (5)(6 + 8)
1
= 2 (5)(14)
= 35
ANSWER
Formula for the area of a triangle
Substitute 5 for h, 6 for b1, and 8 for b2.
Simplify within parentheses.
Simplify.
The area of the trapezoid is 35 square
inches.
Your Turn:
Find the area of the trapezoid.
1.
ANSWER
63 m2
ANSWER
182 ft2
ANSWER
50 cm2
2.
3.
Example 2
Use the Area of a Trapezoid
Find the value of b2 given that the area
of the trapezoid is 96 square meters.
SOLUTION
1
A = h(b1 + b2)
2
1
96 = (8)(9 + b2)
2
Formula for the area of a trapezoid
Substitute 96 for A, 8 for h, and 9 for b1.
192 = 8(9 + b2)
Multiply each side by 2.
192 = 72 + 8b2
Use the distributive property.
120 = 8b2
Subtract 72 from each side.
15 = b2
ANSWER
Divide each side by 8.
The value of b2 is 15 meters.
Your Turn:
A gives the area of the trapezoid. Find the missing
measure.
1. A = 77 ft2
ANSWER h = 7 ft
2. A = 39 cm2
ANSWER
b1 = 5 cm
3. A = 84 in.2
ANSWER
b2 = 8 in.
4. A trapezoid has an area of 294 square yards. Its
height is 14 yards and the length of one base is 30
yards. Find the length of the other base.
ANSWER
12 yards
Assignment
Pg. 448 – 450: #1 – 15 odd, 19 – 37 odd