What is the surface area of the triangular prism?

Question

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

Answer 1

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.