The given rectangular prism's surface area equals 172 cm².
Step-by-step explanation:
Step 1:
In order to determine the surface area of the complete prism, we need to calculate the areas of all the different colored sections of the prism and sum all of them up. There are a total of 6 different sections in the prism. There are
2 green sections,
2 purple sections, and
2 red sections.
Step 2:
Each square is 1 cm² so the area of each section is the length multiplied with the width. The sections with the same colors have the same areas.
Green sections area = [tex](length) (width) = (7)(8) = 56[/tex] cm².
Purple sections area = [tex](length) (width) = (8)(2) = 16[/tex] cm²,
Red sections area = [tex](length) (width) = (7) (2) = 14[/tex] cm².
Step 3:
Total surface area = Area of the first green section + Area of the first purple section + Area of the second green section + Area of the second purple section + Area of the first red section + Area of the second red section.
Total surface area = [tex]56 + 16 +56 + 16 + 14 + 14 = 172[/tex] cm².
