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October 31st, 2011, 05:30 AM  #1 
Newbie Joined: Oct 2011 Posts: 8 Thanks: 0  Need help to solve one math task
I added attachment, where is plot. Need to know area of the trapezoid (S=?) I hope someone can help me! 
October 31st, 2011, 08:11 PM  #2 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038  Re: Need help to solve one math task
I'll be assuming that angleBOC = 90 degrees, so triangleBOC is a right triangle. If not, then angleBOC needs to be a given (or another given is required), else not enough info. Draw line CE, E on AB, such that CE is parallel to AD; so we now have rectangle AECD and right triangle BCE: the sum of their areas = area of trapezoidABCD. Step#1 : BC = SQRT(4^2 + 2^2) = 2SQRT(5) : ~4.472 Step#2 : angleCBO = ASIN[1 / SQRT(5)] : ~26.565 degrees Step#3: radius = r = 4SIN(angleCBO) : ~1.788 Step#4: draw radius OQ, Q on CD; CQ = SQRT(4  r^2) : ~.894 ; so CD = r + SQRT(4  r^2) Step#5: BE = SQRT[BC^2  (2r)^2] = 2SQRT(5  r^2) : ~2.683 So areaAECD = 2r[r + SQRT(4  r^2)] and areaBCE = 2r[2SQRT(5  r^2)] Area of trapezoid is sum of these 2 areas; simplifies to 2r[r + SQRT(4  r^2) + SQRT(5  r^2)] : exactly 14.4 

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