A trapezoid has an area of 100 square units. What scale factor would be required to dilate the trapezoid to have 400

Answer 1

The ratio of areas (of similar figures) is as the square of the scale factor

s² = 400 / 100

s² = 20 / 10

s = 2

Answer 2

The area of a trapezoid is 1/2(sum of bases)(height)

So, we have (1/2)(b₁ + b₂)h = 100

(1/2)(2b₁ + 2b₂)(2h) = (1/2)(2(b₁ + b₂))(2h) = 4(1/2)(b₁ + b₂)(h) = 4(100) = 400

Doubling each base and doubling the height increases the area by a factor of 4.

In other words, the needed scale factor is 2.