# Area of a trapezoid introduction

How do we describe a trapezoid? A trapezoid is a 4-sided object or shape with a pair of parallel sides. For example, in the diagram used to describe what trapezoid looks like below, its bases are parallel. In order to find the area of a trapezoid, add all its bases together, multiply the sum by its height then divide the answer you get at the end by 2. The formula for the area of a trapezoid is given below:

• Let A stand for area; therefore, area of trapezoid A = (b1 + b2). h2 or A = 12.(b1 + b2). h
• Where b1 represents base1, b2 represents base2 while h represents the height of the trapezoid used in determining the area of trapezoid
• First extend the sides DA and CB of the trapezoid in order to meet at a point O. The area of the trapezoid can then be found by subtracting the area of triangle AOB obtained from the trapezoid from the area of triangle DOC
• ABCD is a trapezoid and its bases AB and DC are parallel. Since AB and DC are parallel, the triangles AOB and DOC are similar hence the proportionality of the corresponding sides, i.e. OA / OD = OB / OC = AB / DC = 78 / 104 = 3 / 4
• Use equation OA / OD = 3 / 4 to determine OA, i.e. OA / (OA + 10) = 3 / 4 = 30
• Use equation OB / OC = 3 / 4 and solve for OA, i.e. OB / (OB + 24) = 3 / 4 = 72
• With the help of Heron’s formula, we can find the area of triangle AOB, i.e. S = 0.5 x (AO + OB + BA) = 0.5 x (30 + 72 + 78) = 90
• area of a trapezoid = square root of [ s(s – AO)(S – OB)(S – BA) ] = square root of [ 90(90 – 30)(90 – 72)(90 – 78) ] = 1080 unit2
• We now use Heron’s formula again to find area of triangle DOC, i.e. S = 0.5 x (DO + OC + CD) = 0.5 x (40 + 96 + 104) = 120
• area of a trapezoid = square root of [ s(s – DO)(S – OC)(S – CD) ] = square root of [ 120(120 – 40)(120 – 96)(120 – 104) ] = 1920 unit2
• Therefore, the area of a trapezoid is: 1920 – 1080 = 840 unit2

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