9'2 Areas of Triangles, Trapezoids and Kites

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9.2 Areas of Triangles, Trapezoids and Kites

• Geometry CP
• Chapter 9 Area

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How would you solve?
Find the area of the triangle
h
h
b
b
b 10 cm h 6 cm
30 cm 2
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Example

• Does the same hold true for this triangle?

h
b
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Conjecture

• C-83 Triangle Area Conjecture
• A b ? h
• A the area
• b the length of the base
• h the height of the triangle

1 2
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How would you solve?
Find the area of the trapezoid
b1
b2

• By copying and flipping, we know the area of
  this new figure

s
h
b1
b2

• Recall
• The parallel sides are called bases
• The altitude is a segment from one base to
  another and perpendicular to both
• The height of a trapezoid is the length of an
  altitude

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Conjecture

• C- 84 Trapezoid Area Conjecture
• A (b1 b2) ? h
• A area
• b1 and b2 parallel sides
• h distance between the bases height

1 2
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How would you solve?
Find the area of a kite
1 2
1 2
d1
d1
d2
Kite Blue triangle red triangle
d1d2
1 2

• Recall
• The diagonal connecting the vertex angles of a
  kite divides the kite into two congruent
  triangles
• The diagonal connecting the nonvertex angles
  divides the kite into two isosceles triangles
• The diagonals are perpendicular to each other and
  divide the kite into 4 right triangles

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Conjecture

• C-85 Kite Area Conjecture
• A ? d1 ? d2
• A area
• d1 and d2 diagonals

1 2
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Homework

• Page 439 -440
• 1-16