What is the surface area of the triangular prism?
Illustration shows long rectangle left to right the end labeled 6cm. In the middle on top is a cone labeled 8cm on both sides with a dotted line down the middle labeled 6.9cm base of that cone is labeled 8cm. There is cone on the bottom as well .answer is in cm
To calculate the surface area of the triangular prism, we first need to find the lateral surface area of the two triangular faces.
Lateral surface area of a triangular prism = Perimeter of base x height
Perimeter of the base triangle = 6 + 8 + 6.9 = 20.9 cm
Height of the triangular prism = 8 cm
Lateral surface area of one triangular face = 20.9 cm x 8 cm = 167.2 cm² (for one face)
Since there are two triangular faces in the prism, the total lateral surface area of the two triangular faces = 2 x 167.2 cm² = 334.4 cm²
Now we need to find the surface area of the two rectangular faces.
Surface area of one rectangular face = 6 cm x 8 cm = 48 cm² (for one face)
Since there are two rectangular faces in the prism, the total surface area of the two rectangular faces = 2 x 48 cm² = 96 cm²
Finally, add the lateral surface area of the two triangular faces and the surface area of the two rectangular faces to find the total surface area of the triangular prism:
Total surface area = 334.4 cm² + 96 cm² = 430.4 cm²
Therefore, the surface area of the triangular prism is 430.4 cm².