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October 31st, 2011, 05:30 AM   #1
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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!
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October 31st, 2011, 08:11 PM   #2
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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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