Find the area of an isosceles trapezoid ABCD with a side CD of length 6 if the distances from vertices

| January 28, 2021 | education

Find the area of an isosceles trapezoid ABCD with a side CD of length 6 if the distances from vertices A and B to line CD are 9 and 5, respectively.

If in the trapezoid we continue straight lines AB and СD to point H, then we get 2 similar triangles AНD and BCH. In these triangles, 2 heights are already indicated, equal to 9 in the ADН triangle and a height equal to 5 in the BCH triangle.

And in such triangles, the heights are also similar. Then:

9: 5 = НD: CH; (НС + СD): СН = 9: 5, whence we find that

5 * HC + 5 * СD = 9 * CH; 4 * НС = 5 * СD. Where do we find the neural network:

НС = 5 * НС: 4 = 5 * 6: 4 = 7.5. НD = СD + НС = 6 + 7.5 = 13.5.

Area s AВСD = s HAD – s ВCH = 1/2 * (HD * 9 – HC * 5) = 1/2 * (13.5 * 9 – 7.5 * 5) = (121.5 – 37.5 ) / 2 = 42 (sq. Units).



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