This lesson allows students to practice using the formula for the area of parallelograms, and to choose the measurements to use as a base and a corresponding height. Through repeated reasoning, they see that some measurements are more helpful than others. For example, if a parallelogram on a grid has a vertical side or horizontal side, both the base and height can be more easily determined if the vertical or horizontal side is used as a base.
Along the way, students see that parallelograms with the same base and the same height have the same area because the products of those two numbers are equal, even if the parallelograms look very different. This gives us a way to use given dimensions to find others.
- Apply the formula for area of a parallelogram to find the area, the length of the base, or the height, and explain (orally and in writing) the solution method.
- Choose which measurements to use for calculating the area of a parallelogram when more than one base or height measurement is given, and explain (orally and in writing) the choice.
Let's practice finding the area of parallelograms.
- I can use the area formula to find the area of any parallelogram.
base (of a parallelogram or triangle)
We can choose any side of a parallelogram or triangle to be the shape’s base. Sometimes we use the word base to refer to the length of this side.
height (of a parallelogram or triangle)
The height is the shortest distance from the base of the shape to the opposite side (for a parallelogram) or opposite vertex (for a triangle).
We can show the height in more than one place, but it will always be perpendicular to the chosen base.
A parallelogram is a type of quadrilateral that has two pairs of parallel sides.
Here are two examples of parallelograms.
A quadrilateral is a type of polygon that has 4 sides. A rectangle is an example of a quadrilateral. A pentagon is not a quadrilateral, because it has 5 sides.