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
The total surface area of the pencil sharpener can be calculated using the formula:
Total surface area = 2 * (area of rectangular sides) + (area of triangular faces)
First, calculate the area of the rectangular sides:
Area of one rectangular side = length * width
Area of one rectangular side = 15 cm * 6 cm
Area of one rectangular side = 90 cm²
Since there are two rectangular sides, the total area of the rectangular sides is:
Total area of rectangular sides = 2 * 90 cm²
Total area of rectangular sides = 180 cm²
Next, calculate the area of one triangular face using the formula:
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 = 18.7725 cm²
Since there are two triangular faces, the total area of the triangular faces is:
Total area of triangular faces = 2 * 18.7725 cm²
Total area of triangular faces = 37.545 cm²
Finally, calculate the total surface area of the pencil sharpener:
Total surface area = 2 * 90 cm² + 37.545 cm²
Total surface area = 180 cm² + 37.545 cm²
Total surface area = 217.545 cm²
Therefore, the total surface area of the pencil sharpener is 217.55 cm².