Let say that the rectangle has sides of length a and b. So the perimeter can be written as follows:
perimeter = a + a + b + b
perimeter = 2a + 2b
or
perimeter = 2(a + b)
I choose a to be the longer side, which is 20 in. So a = 20 in . If the perimeter equals 58, we can solve for b:
58 = 2(20 + b)
29 = 20 + b
29 - 20 = b
b = 9 in
Now we can apply the formula to get the area:
area = a x b
area = 20 x 9
area = 180 in²
Answer: area = 180 in²