1. Areas of Triangles and Special Quadrilaterals
Chapter 6 Section 6.7B
Areas of Triangles and Special Quadrilaterals
Find formulas for the area of triangles, and special quadrilaterals. Use these formulas to find the area of triangles, and special quadrilaterals.

2. AREA POSTULATES
Postulates

3. AREA FORMULA OF A TRAPEZOIDb1 b2
The Shape is a trapezoid. Label the top base b1 and the bottom base b2.

4. b1 should now be on the bottom and b2 should now be on the top.
AREA FORMULA OF A TRAPEZOID b1 b2 b2 b1
Copy the trapezoid upside down to the right of the given one so that they share a common side
b1 should now be on the bottom and b2 should now be on the top.

5. Draw in a height and label it h. Find its length.
AREA FORMULA OF A TRAPEZOID b1 b2 h b2 b1
Notice that the new shape is a parallelogram. Find the length of the bottom base of the parallelogram
Bottom Base = b2 + b1 = 14
Draw in a height and label it h. Find its length.
h = 5

6. Area of the parallelogram A = bh = 14(5) = 70 square units
AREA FORMULA OF A TRAPEZOID b1 b2 h b2 b1
Find the area of the parallelogram using 14 for the base and 5 for the height.
Area of the parallelogram A = bh = 14(5) = 70 square units
Find the area of one trapezoid.
Area of one trapezoid A = ½(70) = 35 square units

7. Find the area of the parallelogram if b = b1 + b2 and h = h A = bh
AREA FORMULA OF A TRAPEZOID b1 b2 h b2 b1
Find the area of the parallelogram if b = b1 + b2 and h = h
A = bh
A = (b1 + b2 )h
What is the area of one trapezoid

8. AREA FORMULA OF A TRAPEZOID
Theorem b2 b1 h

9. Notice that the Kite ABCD is composed of two triangles, ABC and ADC
AREA FORMULA OF A KITE D A B C X
Notice that the Kite ABCD is composed of two triangles, ABC and ADC
Since the diagonals of a Kite are , BX is the height of ABC and XD is the height of ADC
Both triangles have a base of AC

10. Find the area of each triangle and add them together.
AREA FORMULA OF A KITE B C A X D
Find the area of each triangle and add them together.

11. AREA FORMULA OF A KITE B C A X D
Factor out the ½(AC).

12. According to segment addition, BX + XD = BD
AREA FORMULA OF A KITE B C A X D
According to segment addition, BX + XD = BD

13. AREA FORMULA OF A KITE
Theorem d1 d2

14. AREA FORMULA OF A RHOMBUS
Theorem d1 d2

15. The shape is a square A = s2 A = 132 A = 169 square units
USE A FORMULA TO FIND THE AREA
The shape is a square
A = s2
A = 132
A = 169 square units

16. The shape is a triangle A =½bh A = ½(16)(12) A = 96 square units
USE A FORMULA TO FIND THE AREA
The shape is a triangle
A =½bh
A = ½(16)(12)
A = 96 square units

17. The shape is a triangle A =½bh A = ½(12)(10) A = 60 square units
USE A FORMULA TO FIND THE AREA
The shape is a triangle
A =½bh
A = ½(12)(10)
A = 60 square units

18. The shape is a parallelogram A =bh A = (15)(11) A = 165 square units
USE A FORMULA TO FIND THE AREA
The shape is a parallelogram
A =bh
A = (15)(11)
A = 165 square units

19. The shape is a rhombus A = ½d1d2 A = ½(6)(12) A = 36 square units
USE A FORMULA TO FIND THE AREA
The shape is a rhombus
A = ½d1d2
A = ½(6)(12)
A = 36 square units

20. The shape is a trapezoid
USE A FORMULA TO FIND THE AREA
The shape is a trapezoid

21. The shape is a rectangle Need to find the base
USE A FORMULA TO FIND THE AREA
The shape is a rectangle
Need to find the base
Use the Pythagorean Theorem b
A = bh
A = 16(12)
A = 192 square units
b = 202
b = 400
b2 = 256
b = 16

22. The shape is a trapezoid
USE A FORMULA TO FIND THE AREA
The shape is a trapezoid
Square units

23. The shape is a kite A = ½d1d2 A = ½(6)(7) A = 21 square units
USE A FORMULA TO FIND THE AREA
The shape is a kite
A = ½d1d2
A = ½(6)(7)
A = 21 square units

24. Since the diagonals of a rhombus bisect each other, this is 4
USING AREA FORMULAS
The Shape is a Rhombus
A = ½d1d2
64 = ½(16)d2
64 = 8d2
8 = d2
Pythagorean theorem
= x2
= x2
80 = x2
Since the diagonals of a rhombus bisect each other, this is 4

25. The Shape is a Trapezoid
USING AREA FORMULAS
The Shape is a Trapezoid

26. The Shape is a Trapezoid
USING AREA FORMULAS
The Shape is a Trapezoid

27. The unshaded region is a rectangle A = bh = 6(16) = 96 square units
USING AREA FORMULAS
The unshaded region is a rectangle
A = bh = 6(16) = 96 square units
The shaded region is composed of two congruent triangles
A = ½bh 3 6 3

28. The big triangle is composed of 4 congruent triangles
USING AREA FORMULAS
The big triangle is composed of 4 congruent triangles
Find the area of one of them
A = ½bh
A = ½(4)(12) = 24 square units
Area Shaded = 24 square units
Area Unshaded = 3(24) = 72 square units
h = 12 4 4

29. The whole figure is a rectangle Find the area of the whole thing
USING AREA FORMULAS
The whole figure is a rectangle
Find the area of the whole thing
A = bh = 20(8) = 160 square units
The two triangles are congruent 4 10
A = ½bh
A = ½(4)(10) = 20 square units
Area Shaded = 2(20) = 40 u2
Area Unshaded = 160 – 40 = 120 u2 10 4

30. HW #76 Pg , 20-25, 27-31, 35-38, 50-52