Fill blanks to complete formula for surface are of a triangular prism

S.A = ??+ (S1 + S2 + S3)??

1 answer

To complete the formula for the surface area (S.A.) of a triangular prism, the blanks can be filled in as follows:

\[ S.A. = 2 \times A + (S_1 + S_2 + S_3) \times h \]

Where:

  • \( A \) is the area of the triangular base.
  • \( S_1, S_2, \) and \( S_3 \) are the lengths of the three edges of the triangular base.
  • \( h \) is the height (or length) of the prism.

Thus, the completed formula is:

\[ S.A. = 2 \times A + (S_1 + S_2 + S_3) \times h \]

Alternatively, if the intention was to express the surface area more simply, we could also say:

\[ S.A. = (S_1 + S_2 + S_3) \times h + 2 \times A \]

This indicates that the surface area consists of the area of the two triangular bases plus the area of the three rectangular faces formed by extending the triangle along the height of the prism.