Area of Trapezoids
Learn how to calculate the area of trapezoids using the formula with parallel sides and height.
Definition
- = length of the first base (one parallel side)
- = length of the second base (other parallel side)
- = height (perpendicular distance between the bases)
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Worked Examples
Find the area of a trapezoid with bases of 8 cm and 12 cm, and a height of 5 cm.
Write the formula
→ Area formula identified
Identify the values
cm, cm, cm → Values identified
Add the bases
cm → Sum of bases = 20 cm
Multiply by height
→ 100
Divide by 2
→ 50 cm²
Answer: The area is cm²
Common Mistakes
Forgetting to divide by 2
Why it's wrong: The formula requires dividing by 2 because a trapezoid is half of a parallelogram formed by the sum of the bases.
Correct: Always include the division: , not
Using a slant side instead of the height
Why it's wrong: The height must be perpendicular to both bases. The slanted sides are not the height.
Correct: Always use the perpendicular distance between the parallel sides as the height.
Multiplying the bases instead of adding them
Why it's wrong: The formula requires adding , not multiplying.
Correct: Remember: ADD the bases first, then multiply by height, then divide by 2.
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Practice Problems
17 problemsWhat is the formula for the area of a trapezoid?
Why It Matters
- Architecture: Cross-sections of roofs, bridges, and ramps are often trapezoidal
- Construction: Retaining walls, dam faces, and channel cross-sections
- Land surveying: Irregularly shaped plots often contain trapezoidal sections
- Engineering: Many structural components use trapezoidal shapes for stability
- Art and design: Creating balanced compositions with non-rectangular shapes
Real World Applications
Roof Cross-Sections
Many roof designs have trapezoidal cross-sections where calculating area helps determine material needs.
Example:
A roof section has parallel edges of 6 m (top) and 10 m (bottom), with a height of 2.5 m. Area = m²
A shed roof has parallel edges of 4 m and 7 m, with a height of 2 m.
What is the cross-sectional area of the roof?
Step 1: Write the mathematical expression
Calculate:
Swimming Pool Design
Many swimming pools have a trapezoidal shape when viewed from above to fit irregular yard spaces.
Example:
A pool is 8 m at one end, 12 m at the other, and 15 m long (perpendicular distance). Area = m²
A decorative pond has widths of 3 m and 5 m at opposite ends, with a length of 6 m between them.
What is the surface area of the pond?
Step 1: Write the mathematical expression
Calculate:
Key Takeaways
- 1A trapezoid has exactly one pair of parallel sides called bases ( and )
- 2The area formula is
- 3The height () must be perpendicular to both bases
- 4The formula works by finding the average of the two bases, then multiplying by the height
- 5Always remember to divide by 2 at the end
Frequently Asked Questions
Glossary
- Trapezoid
- A quadrilateral with exactly one pair of parallel sides
- Bases
- The two parallel sides of a trapezoid, labeled and
- Height
- The perpendicular distance between the two bases of a trapezoid
- Parallel sides
- Sides that never intersect and remain the same distance apart
Formula Card
Area of a Trapezoid
Add the two bases, multiply by the height, then divide by 2. Variables: $b_1$ and $b_2$ are the parallel sides, $h$ is the perpendicular height.