Answer: 797.4 m²
Step-by-step explanation:
The surface area is just the total of the areas of each face of of a solid. In this solid, we have 2 triangles and 3 rectangles.
Triangles
We know that the two triangles of this solid are congruent, so they will have the same area. Since the area of a triangle is [tex]\frac{1}{2}bh[/tex], two triangles would have an area of [tex]bh[/tex]. Hence, the total area is
[tex]A=9 * 15\\A=135[/tex]
Rectangles
The area of a rectangle is lw, where l is the length and w is the width. Let's find the total area of all of them.
[tex]A=9*16+15*16+17.4*16[/tex]
All of the areas are a product of some number and 16. This makes sense as the length of this prism is 16. We can un-distribute this 16 to make the calculation easier.
[tex]A=16(9+15+17.4)\\A=16(41.4)\\A=662.4[/tex]
Total
We can add both totals to get the total surface area of the solid.
[tex]135+662.4\\=797.4[/tex]
The surface area of this right triangular prism is 797.4 m².
