Parallelogram Formulas (Area, Perimeter)

A parallelogram is a quadrilateral with both pairs of opposite sides parallel and equal. Its area is A = b·h, the base times the perpendicular height; its perimeter is P = 2(a + b), where a and b are adjacent sides.

Parallelogram formulas

Area: $A = b h$
Perimeter: $P = 2(a + b)$

where b = base, h = height (perpendicular to base), a = slanted side, A = area

Area

A = b h

Worked example

A parallelogram with base 8 and height 5 has area 40 square units.

A = b h = 8\cdot 5 = 40

Perimeter

P = 2(a + b)

Interactive parallelogram explorer

Drag a slider (or type a value, or use the arrow keys) and watch the diagram, the results, and the full step-by-step substitution update live.

Base b

Height h

Slanted side a

Area A 40units²

Perimeter P 28units

Step-by-step substitution

A = b · h = 8 · 5 = 40
P = 2(a + b) = 2(6 + 8) = 28

Classroom use: parallelogram formulas

Who it's for: Grades 6–10 · Middle-school students learning parallelogram area and high-school students proving its properties.

Learning objectives

After using this page, students will be able to:

Apply A = bh using the perpendicular height, not the slanted side.
Explain via shearing why the area matches a rectangle on the same base.
Compute the perimeter from the two distinct side lengths.

Suggested classroom activity

The near-universal error is substituting the slant side for the height. Show the explorer with the height annotated in amber, then ask students which measurement they would have used. Naming the mistake before they make it on an assessment is the whole point of this one.

Standards alignment

Aligned to the Common Core State Standards for Mathematics. Codes are given exactly as published so they can be matched against state crosswalks.
Code	Standard
`6.G.A.1`	Find the area of triangles, special quadrilaterals, and polygons by composing or decomposing shapes.
`7.G.B.6`	Solve real-world problems involving area, volume, and surface area of 2-D and 3-D objects.
`HSG.CO.C.11`	Prove theorems about parallelograms.

Free to use and adapt in class under the terms on our license page — no account, no sign-up, no ads. Content last reviewed August 2026.

Related & next steps

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Frequently asked questions

What is the area of a parallelogram?

The area of a parallelogram is A = b·h, the base times the perpendicular height (not the slanted side). A parallelogram with base 8 and height 5 has area 40.

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