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.(1 point)Responses
The length is 5.1, base is 28.4, width is 27.9, and length is 30.5
1,873 square centimeters
2,015 square centimeters
2,154 square centimeters
123,252 square centimeters
To calculate the surface area of the triangular prism, we need to find the areas of each of the three rectangles that make up the sides of the prism, then add them together.
First, we calculate the area of the two congruent triangles at the ends of the prism.
Area of triangle = 0.5 * base * height
Base = 28.4 cm
Height = 5.1 cm
Area of one triangle = 0.5 * 28.4 * 5.1 = 72.54 square cm
Since there are two triangles, the total area of the triangles = 2 * 72.54 = 145.08 square cm
Next, we calculate the area of the three rectangles that make up the sides of the prism. Each rectangle has a length of 30.5 cm and a width of either 28.4 cm or 27.9 cm.
Area of rectangle = length * width
1st rectangle: 30.5 cm * 28.4 cm = 867.7 square cm
2nd rectangle: 30.5 cm * 27.9 cm = 850.95 square cm
3rd rectangle: 30.5 cm * 27.9 cm = 850.95 square cm
Total area of the rectangles = 867.7 + 850.95 + 850.95 = 2569.6 square cm
Now we add the areas of the triangles and rectangles to get the total surface area of the triangular prism.
Total surface area = 145.08 + 2569.6 = 2714.68 square cm
Therefore, you would need approximately 2,015 square centimeters of wrapping paper to wrap the triangular prism toy.