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.

The approximate lateral area of the prism is

Step-by-step explanation:

we know that

The lateral area of the prism is equal to

where

P is the perimeter of the base of the prism

H is the height of the prism

Find the perimeter of the hexagonal base

Remember that the area of the hexagonal base is equal to

where

P is the perimeter

a is the apothem

we have

substitute and solve for P

Find the lateral area

we have

substitute the values

the answer will be b x² +x-1

step-by-step explanation:

for this case we must apply distributive property to the following expression:

the distributive property states that:

then, when applying the property we have to multiply the -2 for each term within the parenthesis: