Question

-25 Points-

Answer 1

Answer:

823.7 m²

Step-by-step explanation:

If a figure A and a figure B are similar, then

$\dfrac{area_A}{area_B}=k^2$    (*)

k - similarity scale

Calculate the similarity scale:

$k=\dfrac{6}{5}$

We have the surface area of the smaller prism 572 m².

Substitute to the formula (*):

$\dfrac{x}{572}=\left(\dfrac{6}{5}\right)^2\\\\\dfrac{x}{572}=\dfrac{36}{25}\qquad\text{cross multiply}\\\\25x=(36)(572)\\\\25x=20,592\qquad\text{divide both sides by 25}\\\\x=823.68\approx823.7\ m^2$