Trapezoid IV

In a trapezoid ABCD (AB||CD) is |AB| = 15cm |CD| = 7 cm, |AC| = 12 cm, AC is perpendicular to BC. What area has a trapezoid ABCD?

Result

S =  110.635 cm2

Solution:

$\dfrac{x}{15} = \dfrac{12-x}{7} \ \\ x = 90⁄11 ≐ 8.181818 \ cm \ \\ y = 12-x = 42⁄11 ≐ 3.818182 \ cm \ \\ \ \\ x' = \sqrt{ 15^2 - x^2 } = 12.572106078127 \ cm \ \\ y' = \sqrt{ 7^2 - y^2 } = 5.8669828364591 \ cm \ \\ \ \\ S = S_1 + S_2+ S_3+ S_4 \ \\ S = x x' / 2 + x'y / 2 + y y'/2 + xy'/2 \ \\ S = (x x' + x'y + y y' + xy')/2 \ \\ S = 110.635 \ cm^2 \ \\$

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