Answer:
823.7 m²
Step-by-step explanation:
If a figure A and a figure B are similar, then
[tex]\dfrac{area_A}{area_B}=k^2[/tex] (*)
k - similarity scale
Calculate the similarity scale:
[tex]k=\dfrac{6}{5}[/tex]
We have the surface area of the smaller prism 572 m².
Substitute to the formula (*):
[tex]\dfrac{x}{572}=\left(\dfrac{6}{5}\right)^2\\\\\dfrac{x}{572}=\dfrac{36}{25}\qquad\text{cross multiply}\\\\25x=(36)(572)\\\\25x=20,592\qquad\text{divide both sides by 25}\\\\x=823.68\approx823.7\ m^2[/tex]
