The base of a lampshade is a regular hexagon with a height of 12 inches for each lateral face. The lateral area is 396 square inches. Determine the length of each side of the base

5.5 inches

Step-by-step explanation:

Since it is a hexagon, there is 6 faces. The total lateral area is 6 times area of one face. The area of one face is 12 times the width so the total is 6*12*width which equals 396. Dividing both sides by 6 gives you 12*width = 66. Dividing both sides by 12 gives you width = 5.5.