The cost to build the exhibit room depends on its area as shown by the following rule. $E(a)=920$ a where a represents the area of the exhibit room and $E(a)$ represents the cost to build the exhibit room

Step 1 ：Given the formula E(a) = 920 * a, where a is the area of the exhibit room in square meters.

Step 2 ：Calculate the cost for an exhibit room with an area of 100 square meters: E(100) = 920 * 100 = \(92,000\)

Step 3 ：\(\boxed{92,000}\) dollars is the cost to build an exhibit room with an area of 100 square meters.