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
+128473 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
