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

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. 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. 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. 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. 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. 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. 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. 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.