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The base of a triangular prism is an isosceles right triangle with a hypotenuse of √50 centimeters. The height of the prism is 8 centimeters. Find the surface area of the triangular prism. Round your answer to the nearest tenth. Please explain step by step

Mar 2, 2022

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Since the right triangle is isosceles.....we need to first find the  equal legs of the right triangle

So we have...[by the Pythagorean Theorem ]

L^2  + L^2  =  50

2L^2    =50

L^2   = 50  / 2

L^2  = 25        take the positive root

L =  5 cm =   the equal legs

The surface area  of  one of the right triangles = (1/2) ( product of the legs)   = (1/2)(5 * 5)  = 25/2  = 12.5 cm^2

But we have two of these  (at the bottom and top)  so the total surface area of top/bottom= 2*12.5 = 25cm^2

The area of  the sides  =  perimeter of the right triangle * height of prism

So   we  have  5 + 5 + sqrt 50  = 10 + sqrt 50  =  perimeter

So  area of sides =   [ 10 + sqrt 50 ] * 8  =  80 + 8 sqrt 50  ≈  136.57  cm^2

So  the total  surface area  =   [ 25  + 136.57 ] cm^2   =  161.57 cm^2

Mar 2, 2022