The sum of the two parallel sides of a trapezoid is 22 cm. The segment that connects the midpoints of the two non-parallel sides divides the area of the trapezoid into two parts, in a ratio of 4:7. What is the product of the lengths of the two parallel sides?
The midpoint segment is (1/2) sum of the parallel bases = 11cm
So..... the height of the trapezoid = h
And the height of each separate trapezoid created by the midpoint line = h/2
Call one of the base lengths x....and the other 22 - x
So call the area of the smaller trapezoid = h ( 11 + x)/2
And the area of the larger trapezoid = h (11 + [22 - x]) /2 = h (33 - x)/2
(7/4) area of the smaller = area of the larger....so....
(7/4)h (11 + x) /2 = h(33 - x) /2
(7/4) (11 + x) = 33 - x
77 + 7x = 132 - 4x
11x = 209
x = 19 cm
And the other base = 22 - 19 = 3cm
So...the product of the bases = 19 * 3 = 57