Make a sketch, dropping perpendiculars from the shorter parallel line to the longer
Let that height be h
You now have a rectangle 24 by h, and two triangles.
One has hypotenuse 6, height of h, let its base be x
The other has hypotenuse 8, height of h, and base of 10-x
from the first triangle:
x^2 + h^2 = 36
from the 2nd:
(10-x)^2 + h^2 = 64
subtract them:
(10-x)^2 - x^2 = 28
100 - 20x + x^2 - x^2 = 28
20x = 72
x = 18/5
then (18/5)^2 + h^2 = 36
h^2 = 36-324/25 = 576/25
h = ± 24/5 , ignoring the negative height
so now you have x = 18/5 and y = 24/5
so find the area of the two triangles, and add that to the area of the rectangle
Found the area of TrapeziumABCD whose parallel side are 14cm and 24cm.its non parallel sides are 8cm and 6cm
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