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