Areas of Triangles, Trapezoids, and Kites

1
Areas of Triangles,Trapezoids, and Kites

• Finding a formula for the area of a triangle
• The base of a triangle is any side of the
  triangle
• The height of a triangle is the length of the
  altitude perpendicular to the base
• If I duplicate a triangle, flip it over and align
  it with the original triangle, what shape is
  formed?
• Can you use the area of the parallelogram to find
  a formula for the area of the original triangle?
• C-77 Triangle Area Conjecture
• The area of a triangle is given by the formula A
  ½bh, where A is the area, b is the length of
  the base, and h is the height of the triangle

2
Areas of Triangles,Trapezoids, and Kites

• Finding a formula for the area of a trapezoid
• The bases of a trapezoid are the two parallel
  sides
• The height of a trapezoid is the length of the
  altitude perpendicular to the bases
• If I duplicate a trapezoid, flip it over and
  align it with the original trapezoid, what shape
  is formed?
• Can you use the area of the parallelogram to find
  a formula for the area of the original
  trapezoid?
• C-78 Trapezoid Area Conjecture
• The area of a trapezoid is given by the formula
  A ½(b1b2)h, where A is the area, b1 and b2 are
  the lengths of the bases, and h is the height of
  the trapezoid

3
Areas of Triangles,Trapezoids, and Kites

• Finding a formula for the area of a kite
• The two diagonals with lengths d1 and d2 are
  shown
• What shapes can you break the kite down into?
• What shape is formed if I duplicate each
  triangle?
• Can you use the area of the rectangle to find a
  formula for the area of the kite?
• C-79 Kite Area Conjecture
• The area of a kite is given by the formula A
  ½d1d2, where A is the area, d1 and d2 are the
  lengths of the diagonals of the kite