these prisms are similar. find the surface area of the larger prism in decimal form.\n5 m\nsurface area.= 90…

Explanation:

Step1: Recall the ratio of surface areas for similar solids

For similar solids, the ratio of their surface areas is the square of the ratio of their corresponding linear dimensions (like side lengths, heights, etc.). Let the scale factor (ratio of corresponding sides of larger to smaller prism) be ( k=\frac{7}{5} ). The ratio of their surface areas ( \frac{SA_{larger}}{SA_{smaller}} = k^{2}=\left(\frac{7}{5}\right)^{2} ).

Step2: Calculate the surface area of the larger prism

We know ( SA_{smaller} = 90\space m^{2} ). So, ( SA_{larger}=SA_{smaller}\times\left(\frac{7}{5}\right)^{2} ). Substitute ( SA_{smaller} = 90 ):

( SA_{larger}=90\times\frac{49}{25} )

First, simplify ( 90\div25=\frac{18}{5} ), then ( \frac{18}{5}\times49=\frac{882}{5} = 176.4 )

Answer:

( 176.4 )