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Results are also pinned to the bottom of your screen.Parallelogram Properties
Area
60
square units
Perimeter
36
units
Formulas Used
Area = base × height = 10 × 6 = 60Perimeter = 2 × (base + side) = 2 × (10 + 8) = 36Slant angle = arcsin(h / a) = arcsin(0.75) = 48.5904°
Quick Answer
To calculate parallelogram properties: Area = base x height. Perimeter = 2 x (base + side). For a parallelogram with base 10, height 6, and side 8: Area = 60 square units, Perimeter = 2 x 18 = 36 units. The height is the perpendicular distance between the bases — it is not the same as the slanted side length.
Key Facts
- Formula: Area = base x height
- Formula: Perimeter = 2 x (base + side)
- Height is the perpendicular distance between bases, always <= side length
- A parallelogram with base 10, height 6, side 8 has area 60 and perimeter 36
- Rectangles are parallelograms with 90-degree angles; rhombuses add four equal sides
- Opposite sides and opposite angles of a parallelogram are always equal
- The slant angle satisfies sin(angle) = height / side
Frequently Asked Questions
How do I calculate the area of a parallelogram?
Multiply the base by the perpendicular height: Area = base x height. A parallelogram with base 10 and height 6 has area 60 square units. The height must be measured at 90 degrees to the base, not along the slanted side.
How do I calculate the perimeter of a parallelogram?
Add the two adjacent sides and double: Perimeter = 2 x (base + side). With base 10 and side 8, the perimeter is 36. Opposite sides are equal, so only two distinct measurements are needed.
Is the height the same as the side length?
No. The height is the perpendicular (90-degree) distance between the two bases. The side is the slanted edge. The height is always less than or equal to the side; they are equal only for a rectangle.
What is the difference between a parallelogram and a rectangle?
Both have two pairs of parallel, equal sides. A rectangle requires four 90-degree angles; a parallelogram generally has two acute and two obtuse angles. Every rectangle is a parallelogram, but not vice versa.
How do I find the slant angle of a parallelogram?
Use the height and side: sin(angle) = height / side, so angle = arcsin(height / side). For height 6 and side 8, the angle is arcsin(0.75) = 48.59 degrees.
Why does shearing a rectangle not change its area?
Shearing keeps the base and the perpendicular height the same, and area = base x height depends only on those two values. Push a deck of cards sideways: the shape slants, but each card keeps its base and height.