Use the image to answer the question.
An illustration shows a 3 D triangular prism with the triangular face as a right triangle. The edges that are not visible are represented by dashed lines. The length and base of the triangular prism measures 12 centimeters and 9 centimeters. The perpendicular side of the triangular face measures 5 centimeters and the hypotenuse measures 13 centimeters.
A wedge of cheese is shaped like a triangular prism. How much plastic wrap is needed to cover the wedge of cheese?
(1 point)
Responses
810 cm2
810 cm squared
330 cm2
330 cm squared
287 cm2
287 cm squared
240 cm2
240 cm squared
Skip to navigation
To find the total surface area of the triangular prism shaped wedge of cheese, we need to calculate the area of all five faces of the prism.
The formula for the total surface area of a triangular prism is:
Total Surface Area = (2 * base area) + (height * perimeter of base)
First, let's find the base area:
Base Area = (1/2) * base * perpendicular height
Base Area = (1/2) * 9 * 5
Base Area = 22.5 cm2
Next, let's find the perimeter of the base:
Perimeter of Base = base + base + hypotenuse
Perimeter of Base = 9 + 9 + 13
Perimeter of Base = 31 cm
Now, let's find the total surface area:
Total Surface Area = (2 * 22.5) + (12 * 31)
Total Surface Area = 45 + 372
Total Surface Area = 417 cm2
Therefore, 417 cm2 of plastic wrap is needed to cover the wedge of cheese.
wrong
I apologize for the mistake. Let's correct it.
To find the total surface area of the triangular prism shaped wedge of cheese, we need to calculate the area of all five faces of the prism.
First, let's find the area of the two triangular faces:
Area of one triangular face = (1/2) * base * height
Area of one triangular face = (1/2) * 9 * 5
Area of one triangular face = 22.5 cm2
Total area of both triangular faces = 2 * 22.5
Total area of both triangular faces = 45 cm2
Next, let's find the area of the three rectangular faces:
The three rectangular faces form a rectangle. To find the area of the rectangle, we calculate the perimeter of the triangular base, which we found to be 31 cm, and the height of the prism, which is 12 cm:
Rectangle area = perimeter * height
Rectangle area = 31 * 12
Rectangle area = 372 cm2
Total surface area = Total area of both triangular faces + Area of the three rectangular faces
Total surface area = 45 + 372
Total surface area = 417 cm2
Therefore, 417 cm2 of plastic wrap is needed to cover the wedge of cheese.