Explore trapezoids and their special types. Learn about isosceles and right trapezoids, area formulas with parallel bases, and practical applications.
A trapezoid is a quadrilateral with exactly one pair of parallel sides. The parallel sides are called bases, and the non-parallel sides are called legs or lateral sides.
Trapezoids are the most general type of quadrilateral with parallel sides, making them useful for many practical applications where you need a shape that transitions between two different widths.
Called the bases (top and bottom)
Called the legs or lateral sides
Perpendicular distance between parallel bases
Two bases + two legs = quadrilateral
P = a + b + c + d
Where a and b are bases, c and d are legs
Example: Bases 10 & 6, legs 5 & 5 → P = 10 + 6 + 5 + 5 = 26 units
A = ½ × (a + b) × h
Where a and b are parallel bases, h is height
Example: Bases 10 & 6, height 4 → A = ½ × (10 + 6) × 4 = 32 square units
💡 Memory Tip: The area formula is the average of the two bases times the height: Average of bases = ½ × (a + b), then multiply by height.
A trapezoid where the two non-parallel sides (legs) are equal in length
Lampshade, picture frames, architectural arches
A trapezoid that has one right angle (90°), making one side perpendicular to both parallel sides
Building facades, ramps, stair profiles
A trapezoid with no special angle or side length relationships
Irregular plots of land, custom containers
Stadium seating sections are trapezoidal to provide good sightlines while maximizing capacity in the available space.
Dam walls are trapezoidal in cross-section - wider at the bottom to resist water pressure and narrower at the top.
Many buckets and containers are trapezoidal to make them stackable and easy to remove from molds during manufacturing.
Trapezoids efficiently transition between different widths, making them ideal for structural design.
Trapezoidal shapes maximize area while fitting irregular boundaries or constraints.
Tapered shapes are easier to remove from molds and create stackable products.
Understanding trapezoids helps with integration, approximating curves, and advanced geometry.
Test your understanding with interactive trapezoid calculators and problem-solving tools.
Review other quadrilateral shapes and compare their properties.