Question

a wooden block in the shape of a rectangular prism is cut into two congruent pieces. which statement best compares the surface areas of the pieces to the surface area of the original block? the surface area of each piece is equal to the surface area of the original block minus the area of the face created by the cut. the surface area of each piece is equal to the sum of half the surface area of the original block plus the area of the face created by the cut. the surface area of each piece is equal to the sum of half the surface area of the original block plus half the area of the face created by the cut. the surface area of each piece is equal to 1/2 the surface area of the original block.

Explanation:

Step1: Analyze surface - area change

When a rectangular prism is cut into two congruent pieces, the total surface area of the two new pieces is the original surface area plus the area of the two new faces created by the cut (since each piece has one of the new faces). So for each piece, its surface area \(S_{new}\) is related to the original surface area \(S_{old}\).
Let the area of the face created by the cut be \(A\). The sum of the surface areas of the two new pieces is \(S_{old}+ 2A\). Then for each piece, \(S_{new}=\frac{S_{old}}{2}+A\)

Answer:

The surface area of each piece is equal to the sum of half the surface area of the original block plus the area of the face created by the cut.