Use the image to answer the question.
An illustration shows a two-dimensional net of a triangular prism with all of its sides open and visible. The net appears as three vertical rectangles joined next to each other. All 4 sides of the middle rectangle are drawn with dashed lines. The width of the rectangles is 6 centimeters. The length of the middle rectangle is 8 centimeters. Two identical triangles adjoin the middle rectangle at the top and bottom with sides each measuring 8 centimeters and the perpendicular height measuring 6.9 centimeters.
What is the surface area of the triangular prism? Round the answer to the nearest tenth.
The surface area of the triangular prism can be calculated by finding the area of each rectangular face and each triangular face, and then adding them together.
The rectangular faces each have an area of 6 cm x 8 cm = 48 cm². There are two of these faces, so the total area of the rectangular faces is 2 x 48 cm² = 96 cm².
The triangular faces each have an area of (1/2) x base x height, which is (1/2) x 8 cm x 6.9 cm = 27.6 cm². There are two of these faces, so the total area of the triangular faces is 2 x 27.6 cm² = 55.2 cm².
Therefore, the total surface area of the triangular prism is 96 cm² + 55.2 cm² = 151.2 cm². Rounded to the nearest tenth, the surface area is 151.2 cm².
To find the surface area of the triangular prism, we need to calculate the areas of the individual faces and then sum them up.
Face 1: The middle rectangle has a length of 8 cm and a width of 6 cm. The area of the middle rectangle is 8 cm * 6 cm = 48 cm^2.
Face 2: The top triangle has a base of 8 cm and a height of 6.9 cm. The area of the top triangle is 0.5 * 8 cm * 6.9 cm = 27.6 cm^2.
Face 3: The bottom triangle has the same dimensions as the top triangle, so the area is also 27.6 cm^2.
Face 4: The two side rectangles have a length of 6 cm and a height of 6.9 cm. The area of each side rectangle is 6 cm * 6.9 cm = 41.4 cm^2. Since there are two side rectangles, their total area is 2 * 41.4 cm^2 = 82.8 cm^2.
Now let's sum up the areas of all the faces: 48 cm^2 + 27.6 cm^2 + 27.6 cm^2 + 82.8 cm^2 = 186 cm^2.
Therefore, the surface area of the triangular prism is approximately 186 cm^2.