Parallelogram

Elementary School

Definition

A 2 dimentional shape made up of two sets of parallel lines. Each set of parallel lines are directly opposite across each other, and do not intercect. A parallelogram can be imagined as a slanted square. Its area is calculated as base x height, where the height is a vertical line perpendicular to the base and the top. An alternative formula for the area is (AB)(AD)sinA or (AB)(BC)sinB

Worked examples

\(\)Area\( = bh = (8)(5) = 40\)

Base is 8, perpendicular height is 5; multiply them to find the area.

\(\)Area\( = (AB)(AD)\sin A = (6)(4)\sin 60^\circ = 24 \cdot \frac{\sqrt{3}}{2} \approx 20.8\)

When you know two adjacent sides and the included angle, use the sine formula.

Common mistakes

\(\)Area\( = (\)base\()(\)slant side\()\) → \(\)Area\( = (\)base\()(\)perpendicular height\()\) Height must be perpendicular to the base, not the slanted side length.
All parallelograms are rectangles. → Rectangles are special parallelograms with right angles. A parallelogram can have any angle; only when angles are 90° is it a rectangle.
\((AB)(BC)\sin B\) always equals \((AB)(AD)\sin A\) → Both formulas give the same area but use different pairs of sides and angles. The sine formula works with any two adjacent sides and their included angle.

Where you'll use it next

You'll apply parallelograms when studying rhombuses, rectangles, and other quadrilaterals, solving coordinate geometry problems, proving theorems with vectors, and computing areas in trigonometry and physics.

Found in 1 StudyPug lesson

Area and Perimeter of Parallelograms: A Complete Guide

Grade 5 Math placeholder

Unlock the secrets of parallelograms! Learn to calculate area and perimeter, explore real-world applications, and sharpen your geometry skills with our comprehensive guide and practice problems.

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