Answer: [tex]128cm^2[/tex]
Step-by-step explanation:
You need to find the ratio of the area.
Knowing that the larger base of smaller trapezoid is 15 centimeters and the larger base of the larger trapezoid is 20 centimeters, you can find the ratio of the area:
[tex]r_{A}=(\frac{20cm}{15cm})^2\\\\r_{A}=\frac{16}{9}[/tex]
Then, to calculate the area of the larger trapezoid, you need to multiply the area of the smaller trapezoid by the ratio of the area.
Therefore you get that the area of the larger trapezoid is:
[tex]A_l=(r_{A})(A_s)\\\\A_l=(\frac{16}{9})(72cm^2)\\A_l=128cm^2[/tex]
