Question

the figure below is a net for a right rectangular prism. its surface area is 246 ft² and the area of some of the faces are filled in below. find the area of the missing faces, and the missing dimension. 8 ft 8 ft 9 ft 72 ft² 27 ft² 72 ft² 27 ft² 9 ft 8 ft 8 ft answer the area of each missing face is ft² the length of each missing edge is ft

Explanation:

Step1: Sum known face - areas

The sum of the given face - areas is $72 + 72+27 + 27=198$ square feet.

Step2: Calculate area of missing faces

The total surface area of the prism is 246 square feet. Let the area of each of the two missing faces be $A$. Then $198 + 2A=246$. Solving for $A$:

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Step3: Find the missing dimension

One side of the missing face is 8 feet. Let the missing dimension be $x$. Since the area of a rectangle is $A = lw$, and $A = 24$ and $l = 8$, then $24=8x$. Solving for $x$ gives $x = 3$ feet.

Answer:

The area of each missing face is 24 ft²
The length of each missing edge is 3 ft