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Area of a Trapezoid


A trapezoid is a four-sided polygon with only one pair of parallel sides. A parallelogram is a type of trapezoid that has two pairs of parallel sides.

top base (a)bottom base(b)height


Area - A quantity that expresses the extent of a two-dimensional shape.
Parallelogram - A four-sided polygon with opposite sides parallel.
Polygon - A plane figure with at least three sides.
Trapezoid - A quadrilateral with only one pair of parallel sides.


Area of a Trapezoid Formula Area=a+b2h ext{Area} = rac{a+b}{2} * h

where a is the top base, b is the bottom base, and h is the height of the trapezoid. Note that a+b2 rac{a+b}{2} is the average length of the top and the bottom and that if a=b, the area becomes a*h, which is the area of a parallelogram.

If a trapezoid has a base of length 4, top of length 6, and height of 2, for example, the area is

Area=a+b2×h ext{Area} = rac{a+b}{2} imes h

Area=4+62×2 ext{Area} = rac{4+6}{2} imes 2

Area=5×2 ext{Area} = 5 imes 2

Area=10 ext{Area} = 10


Area of a Trapezoid

Area=12(Base1 + Base2)Height\text{Area} = \dfrac{1}{2} * (\text{Base1 + Base2}) * \text{Height}
Area=12(10+14)10\text{Area} = \dfrac{1}{2} * (10 + 14) * 10
Area=122410\text{Area} = \dfrac{1}{2} * 24 * 10
Area=120\text{Area} = 120

Area of a Trapezoid Worksheets (PDF)

Area of a Trapezoid Worksheet 1

Area of a Trapezoid Worksheet 2

Area of a Trapezoid Worksheet 3