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
of a square centimeter.
The surface area of a triangular prism is given by the formula:
SA = 2B + PH
Where B is the area of the base (a triangle) and PH is the perimeter of the base (the perimeter of the rectangle) times the height of the prism.
First, we need to find the area of the base. Since the base is a triangle, we can use the formula for the area of a triangle:
B = (1/2)bh
Where b is the base of the triangle (which is 8 cm) and h is the height of the triangle (which is 6.9 cm).
B = (1/2)(8 cm)(6.9 cm) = 27.6 cm²
Next, we need to find the perimeter of the base, which is just the perimeter of the middle rectangle:
P = 2L + 2W = 2(8 cm) + 2(6 cm) = 28 cm
Finally, we can plug in the values we've found into the formula for the surface area:
SA = 2B + PH = 2(27.6 cm²) + (28 cm)(6.9 cm) ≈ 415.2 cm²
Rounding to the nearest tenth, we get:
SA ≈ 415.2 cm² ≈ 415.1 cm²
Surface Area of Triangular Prisms Quick Check
What is the formula for the surface area of a triangular prism?
The formula for the surface area of a triangular prism is:
SA = 2B + PH
where B is the area of the base (a triangle) and PH is the perimeter of the base (the perimeter of the rectangle) times the height of the prism.
that's wrong
I apologize for the mistake. The correct formula for the surface area of a triangular prism is:
SA = (perimeter of base) x (height of prism) + 2 x (area of base)
where the base is a triangle.
i meant SA ≈ 415.2 cm² ≈ 415.1 cm² is wrong
I apologize for the confusion. The correct answer is:
SA ≈ 193.8 cm²
I made a mistake in my earlier explanation. The correct perimeter of the rectangular base is actually P = 2L + 4W = 2(8 cm) + 4(6 cm) = 32 cm. Plugging this value into the formula for the surface area, we get:
SA = (32 cm)(6.9 cm) + 2(27.6 cm²) ≈ 193.8 cm²
Thank you for bringing the error to my attention.
can you round that to the nearest tenth?
Yes, rounding the answer to the nearest tenth gives:
SA ≈ 193.8 cm² ≈ 193.8 cm²