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 for the surface area of a prism:
Surface Area = 2(Base Area) + (Perimeter of Base) x (Height)
The triangular base of the prism has an area of 1/2 x base x height.
Base Area = 1/2 x 6.5 cm x 5.77 cm = 18.7825 cm²
The perimeter of the triangular base is the sum of the three sides:
Perimeter = 6.5 cm + 6 cm + 6.5 cm = 19 cm
Now, calculate the total surface area:
Surface Area = 2(18.7825 cm²) + 19 cm x 15 cm
Surface Area = 37.565 cm² + 285 cm²
Surface Area = 322.565 cm²
Therefore, the total surface area of the pencil sharpener is 322.57 cm².
No
Apologies for the mistake in my calculation.
The surface area of the triangular prism can be calculated as follows:
1. The lateral surface area:
Lateral Surface Area = Perimeter of the base x Height
Perimeter of the base = 6.5 cm + 6 cm + 6.5 cm = 19 cm
Height of the prism = 15 cm
Lateral Surface Area = 19 cm x 15 cm = 285 cm²
2. Area of the two triangular faces:
Area of one triangular face = 0.5 x base x height
Area of one triangular face = 0.5 x 6 cm x 5.77 cm = 17.31 cm²
Area of two triangular faces = 2 x 17.31 cm² = 34.62 cm²
Now, Total Surface Area = Lateral Surface Area + 2 x Area of triangular faces
Total Surface Area = 285 cm² + 34.62 cm² = 319.62 cm²
Therefore, the total surface area of the pencil sharpener is 319.62 cm².