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Home Q & A Board Science-Related Homework Help Mathematics
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lee_4123 lee_4123
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11 years ago
Two regular quadrilateral vinyl tiles each of 1ft sides overlap each other such that the overlapping region is a regular octagon. What is the area of the overlapping region?

Please help me with this and show the solution... Thanks!
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#1
11 years ago
Let xsqrt(2) be the side length of the octagon.
2x+xsqrt(2) = 1
x = 1/(1+sqrt(2))
area = 1 - 8[(1/2)x^2] ft^2

Can you finish it now?
wrote...
#2
11 years ago
When you draw it, you can see that, using 45-45-90 triangles, that one side is
sqrt2 x/2 +x +sqrt2 x/2 =sqrt2x +x =11
x(sqrt2 +1) =11
x=11/(sqrt2 +1) =11(sqrt2-1) after rationalizing the denominator
The area of the octagon is 11^2 -4 (area of one 45-45-90 triangle)
since one triangle has area 1/2(xsqrt 2/2)^2 =x^2/4
four triangles =x^2
121 -x^2 =121-121(2 -2sqrt2 +1)
=121-121(3-2sqrt2) =121(2sqrt2 -2 =242(sqrt2-1)
wrote...
#3
11 years ago
A quadrilateral is in a semicircle when end points are joined with centre of circle, then radius will be half a feet. Angle at the centre by one side of octagon is = 360/8= 45 degree and other two angles will be 67.5 degrees. Area of triangle with two adjacent sides of 1/2 feet each and angle between them is 45 degrees. Since it is regular octagon, there fore area of octagon is equal to 8 times the area of one triangle.

      8[(1/2)(0.5)(0.5) sin 45 degree] = sin 45 degree =(sq rt 2)/2 =0.707 ft^2...................Ans
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