Area of a a parallelogram

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

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

• 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

Area of a parallelogram

•A = bh• Where b is the length of the

base and h is the perpendicular height

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

•A = bh

Find the area of each of the following:

• Square rectangle

3 yd.

3 yd. 22 in.

12 in.

parallelogram15 ft

9 ft.8 ft.

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

b2

h

Area of a trapezoid

•A = 1/2 (b1 + b2 ) h

• Where b1 and b2 are the bases and h is the perpendicular height

Finding areas of trapezoids

20 in

28 in.

6 in.

17 in.

24 in.

12 in.

Rhombus

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

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

Find the area of the rhombus

• Use the parallelogram formula or the diagonal formula

5 ft

6 ft30 in

11 in.