A shipping tube is shaped like a triangular prism. The bases are equilateral triangles with edges of 6 inches and a height of 5.2 inches. The tube is 14 inches long. Find the lateral surface area of the shipping tube.
Accepted Solution
A:
the lateral surface area of the prism can be calculated by taking the sum of the area of the three lateral rectangle faces around. 3 rectangle faces - length - 14 inches width is the hypotenuse of the triangle at the base. using Pythagoras theorem, if H - hypotenuse A - height of the triangle at the base (5.2 inches) B - half the length of the side of the equilateral triangle (6/2 = 3 inches) H² = A² + B² H² = 5.2² + 3² = 27.04 + 9 = 36.04 H = 6.00 inches hypotenuse is the width area of rectangle = 14 inches x 6 inches = 84 inch² there are three rectangle faces = 84 x 3 = 252 inch²