A parallelogram is a four-sided shape whose opposite sides are parallel. Its opposite sides are also equal in length, its opposite angles are equal, and its diagonals cut each other in half. Rectangles, rhombuses and squares are special parallelograms. Its area is base times height: A = bh.
Matching tick marks show that opposite sides are equal. The area uses the dashed height, not the slanted side: 8 × 5 = 40.
Formal definition and notation
A parallelogram is a quadrilateralABCD with AB ∥ DC and AD ∥ BC. From this it follows that opposite sides are congruent, opposite angles are congruent, consecutive angles are supplementary (they add to 180°), and the diagonals bisect each other. Conversely, a quadrilateral with either pair of these properties is a parallelogram.
Symbol
Read it as
Meaning
ABCD
parallelogram A B C D
vertices named in order around the shape
AB ∥ DC
segment A B is parallel to segment D C
one pair of opposite sides is parallel
tick marks
tick marks
sides with the same number of ticks have equal length
arrowheads on sides
parallel marks
sides with matching arrowheads are parallel
Key facts
Opposite sides are parallel and equal in length.
Opposite angles are equal, and any two angles next to each other add to 180°. All four angles add to 360°.
The diagonals cut each other in half (they bisect each other). They are equal in length only when the parallelogram is a rectangle.
A rectangle is a parallelogram with four right angles; a rhombus is a parallelogram with four equal sides; a square is both.
Area uses the height, which meets the base at a right angle: A = bh. The slanted side is not the height.
Parallelogram formulas
Parallelogram formulas
A = b × h
b
the base: any side you choose
h
the height: the perpendicular distance from the base to the opposite side, not the slanted side
P = 2a + 2b
perimeter, where a and b are two sides that meet at a corner
Cut the triangle off one end and slide it to the other end: the parallelogram becomes a rectangle with the same base and height. That is why the area is base times height.
Parallelogram examples, step by step
Example 1: Area from base and height
Warm-up
A parallelogram-shaped garden bed has a base of 9 meters and a height of 4 meters. What is its area?
A trapezoid (US definition) has exactly one pair of parallel sides; a parallelogram has two pairs. Trapezoid area averages the two bases: b1 + b22 × h.
A rhombus is a parallelogram with all four sides equal. A general parallelogram only has opposite sides equal, such as 10, 6, 10, 6.
Quick check: 3 questions
Question 1 of 3
A parallelogram has a base of 12 cm, a slanted side of 7 cm and a height of 5 cm. What is its area?
Show answer and explanation
Answer: C.A = bh = 12 × 5 = 60. Choice A multiplies the base by the slanted side, B is the perimeter 2(12 + 7), and D takes half, as for a triangle.
Question 2 of 3
Which statement is true for every parallelogram?
Show answer and explanation
Answer: A. Every parallelogram has diagonals that cut each other in half. Equal diagonals happen only in rectangles, four equal sides only in rhombuses, and four right angles only in rectangles.
Question 3 of 3
One angle of a parallelogram is 135°. What is the angle next to it?
Show answer and explanation
Answer: D. Neighboring angles add to 180°: 180 − 135 = 45. Choice A is the opposite angle, B subtracts from 360, and C assumes a rectangle.
Parallelogram: frequently asked questions
Is a rectangle a parallelogram?
Yes. A rectangle has two pairs of parallel opposite sides, so it meets the definition of a parallelogram. It is a special parallelogram whose four angles are all right angles. A square is also a parallelogram, and so is a rhombus. The reverse is not true: most parallelograms are not rectangles, because their angles are not 90 degrees.
How do you find the area of a parallelogram?
Multiply the base by the height: A = bh. The height is the straight-up distance from the base to the opposite side, measured at a right angle, not the length of the slanted side. A parallelogram with base 8 and height 5 has area 40 square units, the same as an 8 by 5 rectangle.
Is a trapezoid a parallelogram?
Not under the usual US school definition. A trapezoid has exactly one pair of parallel sides, while a parallelogram needs two pairs. Some textbooks use an inclusive definition (at least one pair), and under that definition every parallelogram counts as a trapezoid. Check which definition your class or test uses.
Updated November 2026·Reviewed by the Effortless Math team·Standards: CCSS 3.G.A.1, CCSS 6.G.A.1, CCSS HSG-CO.C.11
Cite this entry
Effortless Math Team. “Parallelogram.” Effortless Math Dictionary. Updated November 2026. https://www.effortlessmath.com/math-dictionary/parallelogram/
Flashcard
TermParallelogramtwo pairs of parallel sides
DefinitionA quadrilateral with opposite sides parallel and equal. Area is base times height: base 8, height 5 gives A = 40.
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