1. Trapezoids and Area of Irregular Shapes
Notes 8-6 and 11-4
Trapezoids and Area of
Irregular Shapes

2. 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

3. What is an Isosceles Trapezoid?
Definition: Trapezoid with congruent legs.
Theorem: Each pair of base angles are congruent.
Theorem: The diagonals are congruent.

4. Example:
Find mF.
mF = 131°

5. Example:
JN = 10.6, and NL = Find KM.
KM = = 25.4

6. Example:
Find the value of a so that PQRS is isosceles.
a = 9 or a = –9

7. Example:
AD = 12x – 11, and BC = 9x – 2. Find the value of x so that ABCD is isosceles.
x = 3

9. Example: Finding Measurements of Trapezoids
Find the area of a trapezoid in which b1 = 8 in.,
b2 = 5 in., and h = 6.2 in.
A = 40.3 in2

10. Example: Finding Measurements of Trapezoids
Find b2 of the trapezoid, in which A = 231 mm2.
b2 = 19 mm

11. Example:
Find the area of the triangle.
A = 96 m2

12. 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)

13. Median of a Trapezoid: (Median)
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.
(Median)

14. Example: Finding Lengths Using Midsegments
Find EF.
EF = 10.75

15. Example:
Find EH.
8 = EH

16. Lesson Quiz:
Use the diagram for items 1 and 2.
1. mWZY = 61°. Find mWXY.
2. XV = 4.6, and WY = Find VZ.
3. Find LP.
119°
9.6 18

17. Example: Finding the Areas of Composite Figures
Find the shaded area. Round to the nearest tenth, if necessary.

18. Example: Finding the Areas of Composite Figures
Find the shaded area. Round to the nearest tenth, if necessary.
shaded area:
= 65 ft2

19. Example:
Find the shaded area. Round to the nearest tenth, if necessary.
Total shaded area is about m2.

20. Example: Finding the Areas of Composite Figures
Find the shaded area. Round to the nearest tenth, if necessary.
area of figure:
234 –  ≈ ft2

21. Example: Finding the Areas of Composite Figures
Find the shaded area. Round to the nearest tenth, if necessary.
area of figure:
100 –128  cm2

22. Example:
Find the shaded area. Round to the nearest tenth, if necessary.
area of figure: 28.3 – 18 = 10.3 in2

23. Example: Fabric Application
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?