Lauretta J. Fox
A trapezoid is a quadrilateral that has exactly two parallel sides. The parallel sides are called the bases of the trapezoid. An altitude of a trapezoid is a segment drawn from a point on one base perpendicular to the other base.
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ABCD is a trapezoid. AB and DC are the bases. DE is an altitude.
A formula to find the area of ABCD may be obtained as follows:
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Draw diagonal DB.
Draw altitude BF perpendicular to DC extended.
Area of ABCD =Area of ’ ABD+ Area of ’ BCD.
Area of ’ ABD = 1/2 x AB x DE
Area of ’ BCD =l/2 x DC x BF
Area of ABCD =l/2 x AB x DE+ 1/2 x DC x EF
DE = BF
Area of ABCD = 1/2 x AB x DE + 1/2 x DC x DE
Area of ABCD= 1/2 x DE x (AB+ DC)
Area of ABCD =l/2 x altitude x (Base l+ Base 2)
The area of a trapezoid equals one half the product of the altitude and the sum of the bases.
Area of a trapezoid 1/2h(b1+b2)
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Example
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Find the area of a trapezoid whose bases are 8 in. and 12 in. and whose altitude is 10 in. long.
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Solution
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A=1/2h(b1+b2) A=1/2x10x(8+12)=5x20=100 sq.in.
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Find the areas of the following trapezoids:
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Complete the following table:
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