Area of Trapezoids

Goal

Find the area of trapezoids.

Key Vocabulary

TrapezoidBase of a trapezoidHeight 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.

b1=base 1

b2=base 2

h=height

What is the area of this triangle?What is the area of

this trapezoid?

Area of Trapezoid

COPY THIS!

h=height

b2=base 2

b1=base 1

What is the area of this trapezoid?

Area of Trapezoid

PASTE HERE!

h=height

b2=base 2

b1=base 1

What is the area of this trapezoid?

Area of Trapezoid

h=height

FLIP VERTICALLY!

b2=base 2

b1=base 1

What is the area of this trapezoid?

Area of Trapezoid

h=height

FLIP HORIZONTALLY!

b2=base 2

b1=base 1

What is the area of this trapezoid?

Area of Trapezoid

h=height

TRANSLATE TO HERE!

b2=base 2

b1=base 1

What is the area of this trapezoid?

Area of Trapezoid

h=height

CHECK MEASUREMENTS!

b2=base 2

b1=base 1

What is the area of this trapezoid?

b1=base 1

Area of Trapezoid

h=height

b2=base 2

b1=base 1

b1=base 1

Area of the trapezoid is ½ the area of this parallelogram?

Area of Trapezoid

h=height

b2=base 2

b1=base 1

b1=base 1

Areatrapezoid = ½ height(base 1 + base 2)

Area of Trapezoid

h=height

b2=base 2

b1=base 1

b1=base 1

Areatrapezoid = ½ h(b1 + b2)

Area of Trapezoid

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.

=12 (5)(6 + 8) Substitute 5 for h, 6 for b1, and 8 for b2.

= 35 Simplify.

ANSWERThe area of the trapezoid is 35 square inches.

=12 (5)(14) Simplify within parentheses.

SOLUTION

Formula for the area of a triangleA = h(b1 + b2)12

Your Turn:

ANSWER 63 m2

Find the area of the trapezoid.

ANSWER 182 ft2

ANSWER 50 cm2

1.

2.

3.

SOLUTION

A = 12 h(b1 + b2) Formula for the area of a trapezoid

Example 2 Use the Area of a Trapezoid

Find the value of b2 given that the area of the trapezoid is 96 square meters.

ANSWER The value of b2 is 15 meters.

120 = 8b2 Subtract 72 from each side.

12 (8)(9 + b2)96 = Substitute 96 for A, 8 for h, and 9 for b1.

15 = b2 Divide each side by 8.

192 = 8(9 + b2) Multiply each side by 2.

192 = 72 + 8b2 Use the distributive property.

Your Turn:

ANSWER h = 7 ft

ANSWER b1 = 5 cm

ANSWER b2 = 8 in.

A gives the area of the trapezoid. Find the missing measure.

1. A = 77 ft2

2. A = 39 cm2

3. A = 84 in.2

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.

4.

ANSWER 12 yards

Assignment

Pg. 448 – 450: #1 – 15 odd, 19 – 37 odd