What is the surface area of the triangular prism? (1 point)
one side has 10cm, one has 8cm, another, is 9cm, and another 6
? square centimeters
To calculate the surface area of the triangular prism, we need to first find the areas of the individual faces and then add them together.
The triangular faces have dimensions:
- Base = 8 cm, Height = 9 cm (8 cm and 9 cm sides)
- Base = 9 cm, Height = 6 cm (9 cm and 6 cm sides)
- Base = 6 cm, Height = 10 cm (6 cm and 10 cm sides)
Using the formula for the area of a triangle (Area = 0.5 x base x height), we can calculate the areas of the triangular faces:
1. Area of the triangular face with sides 8 cm and 9 cm = 0.5 x 8 cm x 9 cm = 36 square cm
2. Area of the triangular face with sides 9 cm and 6 cm = 0.5 x 9 cm x 6 cm = 27 square cm
3. Area of the triangular face with sides 6 cm and 10 cm = 0.5 x 6 cm x 10 cm = 30 square cm
Next, we calculate the area of the rectangular faces (one side is 10 cm x 8 cm, another side is 9 cm x 6 cm, and the last side is 10 cm x 6 cm)
1. Area of the rectangular face with sides 10 cm and 8 cm = 10 cm x 8 cm = 80 square cm
2. Area of the rectangular face with sides 9 cm and 6 cm = 9 cm x 6 cm = 54 square cm
3. Area of the rectangular face with sides 10 cm and 6 cm = 10 cm x 6 cm = 60 square cm
Add all the areas together:
36 + 27 + 30 + 80 + 54 + 60 = 287 square cm
Therefore, the surface area of the triangular prism is 287 square centimeters.