the longer base of a right trapezoid is 12ft. the longer base of a similar right trapezoid is 30ft. The area of the smaller trapezoid is 20ft squared. What is the area of the larger right trapezoid?

For this case, the first thing to do is find the scale factor.
 We have then:
 [tex]k = L1 / L2 [/tex]
 Where,
 L1: side of the largest base of the trapezoid 1
 L2: side of the largest base of the trapezoid 2
 Substituting values:
 [tex]k = 12/30 [/tex]
 Simplifying:
 [tex]k = 6/15 [/tex]
 Then,
 The scale factor can be written as:
 [tex]k ^ 2 = (A1 / A2) [/tex]
 Where,
 A1: area of the smallest trapezoid
 A2: area of the largest trapezoid
 Substituting values we have:
 [tex](6/15) ^ 2 = (20 / A2) [/tex]
 Clearing A2 we have:
 [tex]A2 = (20) * (15/6) ^ 2 A2 = 125 feet ^ 2[/tex]
 Answer:
 The area of the larger right trapezoid is:
 A2 = 125 feet ^ 2