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 30.5 centimeters and 27.9 centimeters. The perpendicular side of the triangular face measures 5.1 centimeter and the hypotenuse measures 28.4 centimeter.
A toy came in a container that is shaped like a triangular prism. How much wrapping paper is needed to wrap the toy? Round your answer to the nearest whole number.
A. 227
B. 2030
C. 5283
D. 8072
To calculate the surface area of the triangular prism (wrapping paper needed to wrap the toy), we need to calculate the surface area of each of the five faces of the prism.
1. The two triangular faces have the same dimensions, so we only need to calculate one of them:
Area of a triangle = (1/2) x base x height
Area = (1/2) x 27.9 cm x 5.1 cm = 71.145 cm^2
Since there are two triangular faces, the total area for both of them is 2 x 71.145 cm^2 = 142.29 cm^2
2. The three rectangular faces:
1st rectangular face: 27.9 cm x 30.5 cm = 851.95 cm^2
2nd rectangular face: 27.9 cm x 30.5 cm = 851.95 cm^2
3rd rectangular face: 30.5 cm x 5.1 cm = 155.55 cm^2
Total area for the three rectangular faces = 851.95 cm^2 + 851.95 cm^2 + 155.55 cm^2 = 1859.45 cm^2
Now, add the total areas of the two triangular faces and three rectangular faces to get the total surface area:
142.29 cm^2 + 1859.45 cm^2 = 2001.74 cm^2
Rounded to the nearest whole number, the wrapping paper needed to wrap the toy would be 2002 cm^2.
Therefore, the answer is B. 2030.