SOLUTION: The question in the text is: The area of a trapezoid is the product of its height and the arithmetic mean of its bases. I know what the answer would be, a general formula. I jus

Question 54895This question is from textbook Roads to Geometry
: The question in the text is: The area of a trapezoid is the product of its height and the arithmetic mean of its bases.
I know what the answer would be, a general formula. I just dont know how to go about getting a written proof for the problem.
Thank you This question is from textbook Roads to Geometry

Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
construct a rectangle by dropping perpendiculars from one parallel side to
the other parallel side. Call the height of the perpendiculars h.
Call the other side l, which is the length of the shortest parallel side.
h*l is the area of this rectangle.
Now you have to find lthe areas of the two triangles that are left.
Call the bases of the triangles x and y. Their heights are both h.
Their areas are
(1/2)*x*h and
(1/2)*y*h
Now add the 3 areas
A = h*l + (1/2)*x*h + (1/2)*y*h
Multiply the 1st term by 2/2. This is OK since 2/2 = 1
A = (2/2)*h*l + (1/2)*x*h + (1/2)*y*h
factor out (1/2)*h
A = (1/2)*h*(2l + x + y)
or, what is the same thing,
A = h*((2l + x + y)/2)
This is what is required. (2l + x + y) can be written (l + x + y + l}
l is one side and x + y + l is the other side
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