Parallelogram
A parallelogram is a quadrilateral with two pairs of parallel sides. Opposite sides are equal in length and opposite angles are equal in measure. The area of a parallelogram is A = base x height, where the height is the perpendicular distance between the parallel sides (not the slant side length). For example, a parallelogram with base 8 cm and height 5 cm has area 40 square centimeters. This 7th grade geometry concept from Saxon Math Course 2 is a building block for understanding trapezoids, rhombuses, and the area formulas of all quadrilaterals.
Key Concepts
Property A quadrilateral with two pairs of parallel sides.
Examples A square is a parallelogram with four equal sides and four $90^\circ$ angles. A rhombus with side length 5 is a parallelogram where all sides are equal.
Explanation Think of a rectangle that's been pushed over! Its opposite sides stay parallel and equal, but the angles aren't necessarily perfect right angles anymore. It's a shape that loves to lean while keeping its opposite sides perfectly aligned, just like a disciplined dancer mid pose.
Common Questions
What is a parallelogram?
A parallelogram is a four-sided figure (quadrilateral) where both pairs of opposite sides are parallel and equal in length. Rectangles and rhombuses are special types of parallelograms.
How do you find the area of a parallelogram?
Area = base x height, where height is the perpendicular distance between the parallel sides. For base 8 cm and height 5 cm: Area = 8 x 5 = 40 square centimeters.
Why is the height not the slant side?
Height must be perpendicular to the base. Using the slanted side gives a longer measurement that overcounts the area. Always use the vertical (perpendicular) height.
What grade studies parallelograms?
Parallelograms are a 7th grade geometry topic in Saxon Math Course 2. Students learn their properties and area formula, connecting to rectangles, rhombuses, and trapezoids.
Is a rectangle a parallelogram?
Yes. A rectangle is a special parallelogram where all four angles are right angles. Since its height equals its width, the area formula A = base x height gives the same result as A = length x width.
What are the properties of a parallelogram?
Opposite sides are parallel and equal. Opposite angles are equal. Consecutive angles are supplementary (add to 180 degrees). Diagonals bisect each other.