Area of a a parallelogram

1
Area of a a parallelogram

• In a parallelogram, the height is a segment
  perpendicular to both bases

2

• If a diagonal is drawn in a parallelogram, 2
  identical triangles are formed.

3

• The area of a parallelogram is twice the area of
  one of the triangles, so an expression to find
  the area of a parallelogram could be written
• A 2 (1/2 bh) which simplifies to
• A bh

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Area of a parallelogram

• A bh
• Where b is the length of the base and h is the
  perpendicular height

5

• Since rectangles, rhombuses, and squares are all
  parallelograms, the area of these shapes can also
  be found using the same formula
• A bh

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Find the area of each of the following

• Square rectangle

3 yd.
12 in.
22 in.
3 yd.
parallelogram
15 ft
9 ft.
8 ft.
7
Trapezoid

• A trapezoid is a quadrilateral with exactly 1
  pair of parallel sides
• The height of the trapezoid is the a segment that
  is perpendicular to both parallel sides of the
  trapezoid- these parallel sides are the bases- b1
  and b2

b1
h
b2
8
Area of a trapezoid

• A 1/2 (b1 b2 ) h
• Where b1 and b2 are the bases and h is the
  perpendicular height

9
Finding areas of trapezoids
28 in.
17 in.
6 in.
12 in.
24 in.
20 in
10
Rhombus

• A rhombus's diagonals are perpendicular and
  bisect each other

11
Area of a rhombus

• Since a rhombus is a parallelogram, you can use
  the formula for parallelogram
• A bh
• Or
• You can use the diagonals formula
• A 1/2 d1 d2
• Where d1 and d2 represent the diagonals of the
  rhombus

12
Find the area of the rhombus

• Use the parallelogram formula or the diagonal
  formula

30 in
6 ft
11 in.
5 ft