The sum of the base and the height of a triangle is 20 centimeters. find the maximum area of the triangle.

The formula for the area of a triangle is A = 1/2bh. If you're told the base + the height = 20, you know the most each could be is 10, cause 10 + 10 = 20.
(It is possible for one of them to be 9 and the other 11 or 8 and 12, etc. but you're looking for the biggest possible area and 10(10) = 100 is bigger than 9(11) or 8(12) which equal 99 and 96)
Multiply the base and height, then divide that answer by 2 (or multiply by 1/2, same thing) to get the area.
10(10) = 100
100/2 = 50
The correct answer would be 50cm².