Posted by **justme** on Saturday, October 15, 2011 at 7:41pm.

Square OPQR has vertices O(0; 0), P(0; 8), Q(8; 8), and R(8; 0). The parabola

with equation y = a(x �� 2)(x �� 6) intersects the sides of the square OPQR at

points K, L, M, and N. Determine all the values of a for which the area of the

trapezoid KLMN is 36.

- math -
**Reiny**, Saturday, October 15, 2011 at 9:48pm
I made a sketch and found the following coordinates

K(0,12a) , L(2,0) , M(6,0) and N(8,12a

so the area of the trapezoid

= (KN + LM)(OK)/2 = 36

(8 + 4)(12a)/2 = 36

144a = 72

a = 72/144 = 1/2

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