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Find the area of the triangular section of the rectangle solid shown in the figure .

Find the area of the triangular section of the rectangle solid shown in the figure-example-1

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Find the area of the triangular section of the rectangle solid shown in the figure-example-1
User Ray Shan
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Length of three diagonal A,B and C of given solid is


A=√(12^2+4^2)\\\\A=√(160)\\\\A=4 √(10)\\\\B=√(12^2+8^2)\\\\B=√(208)\\\\B=4√(13)\\\\C=√(8^2+4^2)\\\\C=√(80)\\\\C=4√(5)

Area of Triangle


=(1)/(2) * \text {Product of two adjacent sides}* \text{Angle between these two sides}


\cos B=(c^2+a^2-b^2)/(2*a*c)\\\\\cos B=(160+80-208)/(2*4√(5)*4√(10))\\\\ \cos B=(32)/(32*√(50))\\\\ \cos B=(1)/(√(50))\\\\\ sin^2B=1-(1)/(50)\\\\ \sin B=(7)/(√(50))\\\\ \text{Area}\Delta=(1)/(2)ac \sin B\\\\=(1)/(2) * 4√(5) * 4√(10)* (7)/(√(50))\\\\=(112)/(2)\\\\\text{Area}\Delta=56 \text{Square Unit}

Find the area of the triangular section of the rectangle solid shown in the figure-example-1
User Msbg
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