Question

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?

Answer 1

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