For example, if you find that the top base (b1) is 8 cm and the bottom base (b2) is 13 cm, the total length of the bases is 21 (8 cm + 13 cm = 21 cm, which reflects the “b = b1 + b2” part of the equation).
The length of the angled sides, or the legs of the trapezoid, is not the same as the height. The leg length is only the same as the height if the leg is perpendicular to the bases.
In this example, 21 cm x 7 cm = 147 cm2 which reflects the “(b)h” part of the equation.
For this example, 147 cm2 / 2 = 73. 5 cm2, which is the area (A).
This method only works for regular trapezoids.
For example, if the top base (b1) is 6 cm and the bottom base (b2) is 12 cm, then the base of the triangle is 3 cm (because b = (b2 - b1)/2 and (12 cm - 6 cm)/2 = 6 cm which can be simplified to 6 cm/2 = 3 cm).
Fill in the variables: (3 cm)2 + B2 = (5 cm)2 Simplify the squares: 9 cm +B2 = 25 cm Subtract 9 cm from each side: B2 = 16 cm Take the square root of each side: B = 4 cm
Write the formula: A = ½(b1+b2)h Fill in the variables: A = ½(6 cm +12 cm)(4 cm) Simplify the terms: A = ½(18 cm)(4 cm) Multiply the numbers together: A = 36 cm2.
