Answer:
284 square cm.
Explanation:
To calculate the total surface area (TSA) of the triangular prism formed by an isosceles triangle and a rectangle, you need to find the surface areas of both the triangular faces and the three rectangular faces and then add them together.
1. **Triangular Faces**:
You have an isosceles triangle with a base of 6 cm and a height of 4 cm. The total area of both triangular faces can be calculated using the formula for the area of a triangle:
Area of one triangular face = (1/2) * base * height
Area of one triangular face = (1/2) * 6 cm * 4 cm = 12 square cm
Since there are two identical triangular faces, the total area of both triangular faces is 2 * 12 square cm = 24 square cm.
2. **Rectangular Faces**:
You have a rectangular prism with dimensions 10 cm x 10 cm x 6 cm. There are three rectangular faces.
- The two rectangular faces with dimensions 10 cm x 10 cm have an area of 100 square cm each.
- The third rectangular face with dimensions 6 cm x 10 cm has an area of 60 square cm.
The total area of all three rectangular faces is 2 * 100 square cm + 60 square cm = 260 square cm.
3. **Total Surface Area (TSA)**:
Now, you can calculate the TSA of the triangular prism by adding the areas of the triangular faces and the areas of the rectangular faces:
TSA = Area of Triangular Faces + Area of Rectangular Faces
TSA = 24 square cm + 260 square cm = 284 square cm
So, the total surface area of the triangular prism is 284 square cm.