SOLUTION: I have 2 triangles in a trapezoid. there is an "X" in the trapezoid coneecting corners and I need to find the height of 2 verticle triangles ( >< ) and one has the base of nine and

Algebra ->  Triangles -> SOLUTION: I have 2 triangles in a trapezoid. there is an "X" in the trapezoid coneecting corners and I need to find the height of 2 verticle triangles ( >< ) and one has the base of nine and      Log On


   

Question 142911: I have 2 triangles in a trapezoid. there is an "X" in the trapezoid coneecting corners and I need to find the height of 2 verticle triangles ( >< ) and one has the base of nine and the other a base of 15 (the bases of the triangles are the parallel lines in the trapezoid which has an area of 27) I need to find the height of a triangle with the base of 15!
Answer by psbhowmick(878) About Me  (Show Source):
You can put this solution on YOUR website!

Let the trapezoid be ABCD.
Given: AB = 15 units, CD = 9 units, Area of trapezoid ABCD = 27 sq units.
Draw CE, perpendicular to AB from C at E. Let CE = h units.
Observe that CE is the height for both the triangles ABC and ACD as their bases are parallel.

Area of trapezoid ABCD
= Area of triangle ABC + Area of triangle ACD
= %281%2F2%29+x+15+x+h+%2B+%281%2F2%29+x+9+x+h sq units [since AREA+=+1%2F2xBASExALTITUDE]
= %281%2F2%29%2815h+%2B+9h%29 sq units
= %281%2F2%2924h sq units
= 12h sq units

But area of trapezoid ABCD is given to be 27 sq units.
So, 12h+=+27
h+=+9%2F4+=+2.25 units

Thus, required height is 2.25 units.