Trapezoid Area Calculator
Calculate the area of a trapezoid using the two parallel sides and height: A = ½(a + b) × h
Enter Parallel Sides and Height
Step-by-Step Solution:
1. Formula: Area = ½ × (a + b) × h
2. Add parallel sides: 6 + 10 = 16
3. Multiply by height: 16 × 5 = 80
4. Multiply by ½: 80 × 0.5 = 40.00 square units
Trapezoid Area Formula
Area = ½ × (a + b) × h
where: - a = length of the top parallel side - b = length of the bottom parallel side - h = perpendicular height between the parallel sides
How to Find Trapezoid Area
- Identify the parallel sides: Find the two sides that are parallel to each other (called bases)
- Measure both bases: Record the length of each parallel side (a and b)
- Find the height: Measure the perpendicular distance between the two parallel sides
- Add the bases: Calculate a + b
- Multiply by height: Multiply the sum by h
- Divide by 2: Multiply the result by ½ to get the final area
Why the Formula Works
The trapezoid area formula works because ½(a + b) gives the average length of the two parallel sides. This average, multiplied by the height, produces the same area as if the trapezoid were a rectangle with that average width. You can also think of it as cutting the trapezoid into two triangles: one with base a and one with base b, both sharing the same height h.
Real-World Applications
Trapezoid area calculations are used in: - Architecture: Calculating roof areas and wall sections - Civil engineering: Cross-sections of roads and channels - Land surveying: Irregularly shaped plots of land - Construction: Estimating material for trapezoidal surfaces - Graphic design: Laying out trapezoidal shapes and frames
Common Questions
What is the formula for trapezoid area?
The trapezoid area formula is A = ½ × (a + b) × h, where a and b are the two parallel sides and h is the perpendicular height between them.
Why does the trapezoid formula use the average of the two bases?
The formula ½(a + b) calculates the average length of the two parallel sides. Multiplying this average by the height gives the area, because a trapezoid can be thought of as a rectangle with that average width.
What is the difference between a trapezoid and a parallelogram?
A trapezoid has exactly one pair of parallel sides, while a parallelogram has two pairs of parallel sides. A parallelogram is a special case of a trapezoid where both pairs of opposite sides are equal and parallel.