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 Algebra Pre-Algebra and Basic Algebra Math Forum

October 31st, 2011, 05:30 AM   #1
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Joined: Oct 2011

Posts: 8
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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!
Attached Images math.jpg (20.8 KB, 100 views) October 31st, 2011, 08:11 PM #2 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1039 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 Tags math, solve, task Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post seyli1234 Calculus 1 February 1st, 2014 09:54 AM PLUS-MINUS Algebra 2 December 23rd, 2013 05:34 PM grayfox Algebra 3 February 19th, 2013 03:37 PM iiniiniin New Users 0 August 9th, 2010 06:45 AM Gushidd Algebra 0 May 30th, 2009 12:52 PM

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