Question
The ratio of length of two parallel sides is 1 : 3 of a
trapezium while non-parallel sides are in the ratio of 2 : 3. If the ratio of length of larger parallel side to the larger non-parallel side is 2 : 1. Find the area of the trapezium. If its height is (15√15)/4 cm?Solution
Area of triangle = S = (a+b+c)/2 = (2x+3x+4x)/2 = 9x/2 Area = √(s(s-a)(s-b)(s-c)) = √(9x/2 × s/2 x × 9/2 x × x/2) = (3√15)/4 x² Again area of triangle = 1/2 × 4x × (15√15)/4 Compare both areas 1/2 × 4x × (15√15)/4 = (3√15)/4 x² x = 10 cm ∴ Area of trapezium = 1/2 × (2x + 6x) × (15√15)/4 = 1/2 × 8 × 10 × (15√15)/4 = 150√15 cm²
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