Subjects geometry

Triangular Prism Sa 2621E6

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1. The problem is to find the formula for the surface area (SA) of a triangular prism. 2. A triangular prism has two triangular bases and three rectangular faces connecting the corresponding sides of the triangles. 3. The surface area formula is: $$SA = 2B + Ph$$ where $B$ is the area of the triangular base, $P$ is the perimeter of the triangular base, and $h$ is the height (length) of the prism. 4. To find $B$, use the formula for the area of a triangle. For example, if the base of the triangle is $b$ and the height of the triangle is $h_t$, then: $$B = \frac{1}{2} b h_t$$ 5. The perimeter $P$ is the sum of the lengths of all three sides of the triangular base. 6. Multiply the perimeter $P$ by the prism height $h$ to get the total area of the three rectangular faces. 7. Add twice the base area $2B$ to the lateral area $Ph$ to get the total surface area. This formula accounts for all faces of the triangular prism.