Area of a Parallelogram
Area of a parallelogram in Grade 8 Saxon Math Course 3 is calculated using the formula A = base x height, where height is the perpendicular distance between the two parallel bases, not the slant side length. Students learn to identify the correct height and apply the formula to various parallelogram orientations. This foundation supports deriving area formulas for triangles and trapezoids.
Key Concepts
New Concept To find the area of a parallelogram, we multiply the perpendicular base and height. The formula for the area of a parallelogram is: $$A = bh$$ What’s next This is just the foundation. Soon, we'll use worked examples to find the area of parallelograms and explore how area is affected by dilations.
Common Questions
What is the formula for the area of a parallelogram?
Area = base x height, where the height is the perpendicular distance between the two parallel bases. This is the same formula as a rectangle.
How is the height of a parallelogram different from its side length?
The height is the perpendicular distance between the bases, which may be inside or outside the figure. The slant side is not the height unless the angle is 90 degrees.
How is the area of a parallelogram related to a rectangle?
A parallelogram can be rearranged into a rectangle with the same base and height by cutting a triangular piece from one end and attaching it to the other. This shows they have equal areas.
If a parallelogram has base 8 cm and height 5 cm, what is its area?
Area = 8 x 5 = 40 square centimeters. Only the perpendicular height is used, not any slant measurement.
How does Saxon Math Course 3 teach parallelogram area?
Saxon Math Course 3 derives the area formula by showing how a parallelogram transforms into a rectangle, then applies the formula in practice problems with labeled diagrams.