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
287 cm2
287 cm squared
240 cm2
240 cm squared
810 cm2
810 cm squared
330 cm2
To find the total surface area of the triangular prism, we need to find the area of the two triangular faces and the three rectangular faces.
Area of a triangular face = 1/2 * base * height
Area of first triangular face = 1/2 * 9 * 5 = 22.5 cm^2
Area of second triangular face = 22.5 cm^2
Area of a rectangular face = base * height
Area of first rectangular face = 12 * 5 = 60 cm^2
Area of second rectangular face = 12 * 5 = 60 cm^2
Area of third rectangular face = 9 * 12 = 108 cm^2
Total surface area = 2(22.5) + 2(60) + 108 = 45 + 120 + 108 = 273 cm^2
Therefore, 273 cm^2 of plastic wrap is needed to cover the wedge of cheese.