# math

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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 -

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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