Answer:
3620 square units
Step-by-step explanation:
To calculate the surface area of a triangular prism, we need to find the areas of all the individual faces and then sum them up.
A triangular prism has two triangular bases and three rectangular lateral faces.
1. The area of a triangle can be calculated using the formula: Area of a triangle = 1/2 * base * height.
2. The area of a rectangle can be calculated using the formula: Area of a rectangle = length * width.
Given:
- Length of the prism (base of the triangle) = 28
- Width of the prism (side of the triangle) = 25
- Height of the prism (height of the triangle) = 20
First, let's calculate the area of the triangular base:
Area of the triangular base = 1/2 * base * height
Area of the triangular base = 1/2 * 28 * 20
Area of the triangular base = 280 square units
Next, let's calculate the area of the three rectangular lateral faces:
1. The lateral face opposite the base has an area of 28 * 20 = 560 square units.
2. The other two lateral faces have an area of 25 * 20 = 500 square units each.
Now, we sum up the areas of all the faces to find the total surface area of the prism:
Total surface area = 2 * (Area of the triangular base) + 3 * (Area of the rectangular lateral faces)
Total surface area = 2 * 280 + 3 * (560 + 500)
Total surface area = 560 + 3060
Total surface area = 3620 square units
Therefore, the surface area of the triangular prism with a length of 28, width of 25, and height of 20 is 3620 square units.