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
