Notes 8-6 and 11-4

Trapezoids and Area of Irregular Shapes

What is a Trapezoid?

• A trapezoid is a quadrilateral with exactly one pair of parallel sides.

• Parallel sides, base• Nonparallel sides, legs • Base angles, two consecutive angles whose

common side is a base

What is an Isosceles Trapezoid?

• Definition: Trapezoid with congruent legs.

• Theorem: Each pair of base angles are congruent.

• Theorem: The diagonals are congruent.

mF = 131°

Example:

Find mF.

Example:

JN = 10.6, and NL = 14.8. Find KM.

KM = 10.6 + 14.8 = 25.4

Example:

Find the value of a so that PQRS is isosceles.

a = 9 or a = –9

Example:

AD = 12x – 11, and BC = 9x – 2. Find the value of x so that ABCD is isosceles.

x = 3

Find the area of a trapezoid in which b1 = 8 in., b2 = 5 in., and h = 6.2 in.

Example: Finding Measurements of Trapezoids

A = 40.3 in2

Example: Finding Measurements of Trapezoids

Find b2 of the trapezoid, in which A = 231 mm2.

b2 = 19 mm

Example:

Find the area of the triangle.

A = 96 m2

To Prove a Quadrilateral is a

Trapezoid:• If given vertices on coordinate plane:

– Prove exactly one pair of opposite sides are parallel (Slope Formula).

– Prove it is Isosceles by showing both legs are congruent (Distance Formula).

• Example: Is Quadrilateral ABCD a Trapezoid? Isosceles Trapezoid?

A(-5, -3), B(-4, 2), C(-1, 4), D(1, 1)

(Median)

Median of a Trapezoid:

• The Median, or midsegment, of a trapezoid is the segment whose endpoints are the midpoints of the legs.

• The Median is parallel to the bases.• The median’s measure is half the sum of the

bases.

Example: Finding Lengths Using Midsegments

Find EF.

EF = 10.75

Example:

Find EH.

8 = EH

Lesson Quiz:

Use the diagram for items 1 and 2.

1. mWZY = 61°. Find mWXY.

2. XV = 4.6, and WY = 14.2. Find VZ.

3. Find LP.

119°

9.6

18

Find the shaded area. Round to the nearest tenth, if necessary.

Example: Finding the Areas of Composite Figures

Find the shaded area. Round to the nearest tenth, if necessary.

Example: Finding the Areas of Composite Figures

shaded area: 40 + 25 = 65 ft2

Example:

Find the shaded area. Round to the nearest tenth, if necessary.

Total shaded area is about 1781.3 m2.

Example: Finding the Areas of Composite Figures

Find the shaded area. Round to the nearest tenth, if necessary.

area of figure:

234 – 10.125 ≈ 202.2 ft2

Example: Finding the Areas of Composite Figures

Find the shaded area. Round to the nearest tenth, if necessary.

area of figure: 100 –128 186.2 cm2

Example:

Find the shaded area. Round to the nearest tenth, if necessary.

area of figure: 28.3 – 18 = 10.3 in2

A company receives an order for 65 pieces of fabric in the given shape. Each piece is to be dyed red. To dye 6 in2 of fabric, 2 oz of dye is needed. How much dye is needed for the entire order?

Example: Fabric Application