The base of a hexagonal prism has an apothem measuring 10 inches and an area of 346.41 square inches. the prism is 12 inches tall. what is the approximate lateral area of the prism? round to the nearest whole number.

a. 139 square inches
b. 416 square inches
c. 693 square inches
d. 831 square inches

we know that

The lateral area of the prism is equal to

where

P is the perimeter of the base

h is the height of the prism

The area of the base is equal to

where

P is the perimeter of the base

a is the apothem

In this problem we have

Step 1

Find the perimeter of the base P

substitute the values and solve for P

Step 2

Find the lateral area

substitute the values

Round to the nearest whole number

therefore

the answer is the option D