Surface area of a triangular prism with a base of 10, height of 8, width of 9, and a side of 6
To find the surface area of a triangular prism, we need to calculate the areas of the two triangular bases and the three rectangular faces.
1. Area of the base triangle:
The area of a triangle is calculated using the formula: A = 0.5 * base * height.
In this case, the base of the triangle is 10 and the height is 8.
So, the area of the base triangle = 0.5 * 10 * 8 = 40 square units.
2. Area of the side triangles:
The side triangles are right triangles with a base of 6 and height of 8.
So, the area of one side triangle = 0.5 * 6 * 8 = 24 square units.
Since there are two side triangles, the total area of both side triangles = 2 * 24 = 48 square units.
3. Area of the rectangular faces:
The three rectangular faces have dimensions of:
- Width = 9, height = 8 (common face between the base and top of the prism)
- Width = 10, height = 6
- Width = 9, height = 6
The area of each rectangular face is calculated as (width * height).
So, the area of the first rectangular face = 9 * 8 = 72 square units.
The area of the second rectangular face = 10 * 6 = 60 square units.
The area of the third rectangular face = 9 * 6 = 54 square units.
The total area of all three rectangular faces = 72 + 60 + 54 = 186 square units.
Therefore, the surface area of the triangular prism = area of base triangle + total area of side triangles + total area of rectangular faces
Surface area = 40 + 48 + 186 = 274 square units.
The surface area of the triangular prism is 274 square units.