Miss Holmes

Area of A Parallelogram

Standard

7.M.3 -Demonstrate an understanding of the concepts and apply formulas and procedures for determining measures, including those of area and perimeter/circumference of parallelograms, trapezoids, and circles. Given the formulas, determine the surface area and volume of rectangular prisms and cylinders. Use technology as appropriate.

Cluster

C3 Geometry

Vocabualry

Base of a parallelogram - the length of any one of the sides

Height of a parallelogram - the perpendicular distance between the side whose length is the base and the opposite side

Objective 

Finding the area of parallelograms 

Lesson 

The Area Formula for Parallelograms:

A = bh

See how the formula works by looking here.

The base and perpendicular height of a parallelogram can be identified as follows:

Any side can be the base, and then the perpendicular height extends from the side parallel to the base to meet a line through the base at a 90° angle.

For a rectangle, the perpendicular height is one of the sides:

If you know the base and perpendicular height of a parallelogram, then you can find the area using this formula:

Area = base × perpendicular height

Another way to think about parallelograms...

If we start with a typical parallelogram, we can make a few alterations to it in order to calculate its area. If we cut it along its height, we can remove a portion that is a right triangle. If we move this right triangle to the opposite side of the figure, it will fit perfectly and create a rectangle.

Since we already know the area of a rectangle (see above) to be A = lw, let us apply it to the newly altered parallelogram. The base of the original parallogram is now the length of the rectangle. The height of the parallelogram is now the width of the rectangle. Using the names base and height instead of length and width, we see that the area of a parallogram is A = bh.

Example