Use the image to answer the question.
An illustration shows a solid triangular prism with length 15 centimeters, width 6 centimeters, perpendicular height of the triangular face 5.77 centimeters, and side of triangular face 6.5 centimeters.
What is the total surface area of the pencil sharpener? Your answer should have two decimal places.
(1 point)
cm2
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The total surface area of the pencil sharpener can be calculated by finding the areas of each of its faces and adding them together.
First, calculate the area of the triangular faces.
Area of one triangular face = 1/2 * base * height
Area of one triangular face = 1/2 * 6.5 cm * 5.77 cm
Area of one triangular face = 18.76 cm2
Since there are two identical triangular faces, the total area of the triangular faces = 2 * 18.76 cm2 = 37.52 cm2
Next, calculate the area of the rectangular faces.
Area of one rectangular face = length * width
Area of one rectangular face = 15 cm * 6 cm
Area of one rectangular face = 90 cm2
Since there are three identical rectangular faces, the total area of the rectangular faces = 3 * 90 cm2 = 270 cm2
Finally, add the areas of the triangular faces and rectangular faces to get the total surface area.
Total surface area = area of triangular faces + area of rectangular faces
Total surface area = 37.52 cm2 + 270 cm2
Total surface area = 307.52 cm2
Therefore, the total surface area of the pencil sharpener is 307.52 cm2.
not right
I apologize for the mistake in my previous calculation. Let's recalculate the total surface area of the pencil sharpener using the given dimensions.
1. Calculate the area of the two triangular faces:
Area of one triangular face = 1/2 * base * height
Area of one triangular face = 0.5 * 6.5 cm * 5.77 cm
Area of one triangular face = 18.7655 cm2
Since there are two identical triangular faces, the total area of the triangular faces = 2 * 18.7655 cm2 = 37.531 cm2
2. Calculate the area of the three rectangular faces:
Area of one rectangular face = length * width
Area of one rectangular face = 15 cm * 6 cm
Area of one rectangular face = 90 cm2
Since there are three identical rectangular faces, the total area of the rectangular faces = 3 * 90 cm2 = 270 cm2
3. Calculate the total surface area:
Total surface area = area of triangular faces + area of rectangular faces
Total surface area = 37.531 cm2 + 270 cm2
Total surface area = 307.531 cm2
Therefore, the correct total surface area of the pencil sharpener is 307.53 cm2.