Base and height
In a parallelogram, the base is one of the parallel sides, and the height is the perpendicular distance between the base and its opposite parallel side. The height is not the slanted side; it must form a 90-degree angle with the base. For a parallelogram with base 12 cm and slant side 10 cm, the height might be 8 cm. Understanding this distinction is crucial for correctly applying the area formula A = base x height. This concept is taught in Chapter 7 of Saxon Math Course 2 as part of 7th grade geometry.
Key Concepts
Property The base is one of the parallel sides of the parallelogram. The height is the perpendicular distance between the base and the opposite side.
Examples In a parallelogram with base 12 cm and a slanted side of 10 cm, the height is a shorter 8 cm. If a rectangular frame 80 inches tall is bumped, its side length stays 80 inches, but its new height becomes shorter, like 75 inches.
Explanation Think of the base as the floor and the height as how tall the parallelogram stands, measured straight up. Don't be fooled by the slanted side; the height always forms a perfect right angle with the base, showing its true 'altitude'!
Common Questions
What is the base of a parallelogram?
The base is any one of the parallel sides of the parallelogram. You can choose either pair of parallel sides as the base, but the height must be measured perpendicular to whichever base you select.
What is the height of a parallelogram?
The height is the perpendicular distance from the base to the opposite side. It forms a 90-degree angle with the base and is usually shorter than the slanted side.
Why is the height not the same as the side of a parallelogram?
The slanted side is longer than the height unless the parallelogram is a rectangle. The height cuts straight across at a right angle, while the side tilts at an angle.
How do you find the area of a parallelogram?
Multiply the base by the height: A = b x h. For a parallelogram with base 12 cm and height 8 cm, the area is 96 square cm.
What are common mistakes with base and height?
The most common mistake is using the slanted side as the height. Always look for the perpendicular distance, which may need to be drawn inside or outside the figure.
Is this concept covered in 7th grade math?
Yes. Saxon Math Course 2 teaches base and height in Chapter 7, where students learn to calculate areas of parallelograms and distinguish height from side length.