Question

consider the original trapezoid and the reduction.
diagram: original trapezoid with top base 13.5 cm, bottom base 16.5 cm, legs 3 cm each; reduced trapezoid with top base 9 cm, bottom base 11 cm, leg a
figures not drawn to scale.
what is the length of side a, in centimeters, on the reduced trapezoid?
○ 1
○ 1.5
○ 2
○ 4.5

Explanation:

Step1: Determine the scale factor

The original trapezoid has a top base of \(13.5\) cm and the reduced trapezoid has a top base of \(9\) cm. The scale factor \(k\) is the ratio of the reduced length to the original length, so \(k=\frac{9}{13.5}=\frac{2}{3}\).

Step2: Apply the scale factor to the original side length

The original side length (the non - parallel side) is \(3\) cm. To find the length of side \(A\) in the reduced trapezoid, we multiply the original side length by the scale factor: \(A = 3\times\frac{2}{3}=2\) cm.

Answer:

2