Obj. 44 Triangles & Quadrilaterals
The student is able to (I can):
• Develop and use formulas for finding the areas of
tri...
area

The number of square units that will
completely cover a shape without
overlapping

rectangle area One of the first a...
We can take any parallelogram and make a
rectangle out of it:

parallelograms

The area formula of a parallelogram is the
...
Example

Find the height and area of the
parallelogram.
18
10

h
6

We can use the Pythagorean Theorem to
find the height:...
We can use a similar process to find out
that the area of a triangle is one-half that
of a parallelogram with the same hei...
A trapezoid is a little more complicated to
set up, but it also can be derived from a
parallelogram:
b1 + b2

h
b2

b1

b1...
A rhombus or kite can be split into two
congruent triangles along its diagonals
(since the diagonals are perpendicular):

...
Example

Find the d2 of a kite in which d1 = 12 in. and
the area = 96 in2.
d1d2
A=
2
12d2
96 =
2
12d2 = 192
d2 = 16 in.
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Obj. 44 Triangles and Quadrilaterals

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Develop and use formulas for finding the areas of triangles and quadrilaterals

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Obj. 44 Triangles and Quadrilaterals

  1. 1. Obj. 44 Triangles & Quadrilaterals The student is able to (I can): • Develop and use formulas for finding the areas of triangles and quadrilaterals
  2. 2. area The number of square units that will completely cover a shape without overlapping rectangle area One of the first area formulas you learned formula was for a rectangle: A = bh, where b is the length of the base of the rectangle and h is the height of the rectangle. h A = bh b
  3. 3. We can take any parallelogram and make a rectangle out of it: parallelograms The area formula of a parallelogram is the same as the rectangle: A = bh (Note: The main difference between these formulas is that for a rectangle, the height is the same as the length of a side; a parallelogram’s side is not necessarily the same as its height.)
  4. 4. Example Find the height and area of the parallelogram. 18 10 h 6 We can use the Pythagorean Theorem to find the height: h = 102 − 62 = 8 Now that we know the height, we can use the area formula: A = ( 18 )( 8 ) = 144 sq. units
  5. 5. We can use a similar process to find out that the area of a triangle is one-half that of a parallelogram with the same height and base: triangles 1 bh A = bh or A = 2 2
  6. 6. A trapezoid is a little more complicated to set up, but it also can be derived from a parallelogram: b1 + b2 h b2 b1 b1 h b2 trapezoids h (b1 + b2 ) 1 A = h ( b 1 + b2 ) or A = 2 2
  7. 7. A rhombus or kite can be split into two congruent triangles along its diagonals (since the diagonals are perpendicular): Rhombi, squares, and kites  Area of one triangle = 1 ( d1 )  1 d2  = 1 d1d2  2 2  4 1  1 Two triangles = 2  d1d2  = d1d2  4  2 (Squares can use the same formula.)
  8. 8. Example Find the d2 of a kite in which d1 = 12 in. and the area = 96 in2. d1d2 A= 2 12d2 96 = 2 12d2 = 192 d2 = 16 in.

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