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. Right Triangle
(1 point)
L: 30.5cm
W: 27.9cm
H: 5.1cm
Side Length from bottom width corner to top height corner: 28.4cm
To calculate the amount of wrapping paper needed, we need to find the surface area of the triangular prism.
The surface area of a triangular prism can be calculated with the formula:
SA = (2 * base area) + (base perimeter * height)
First, let's calculate the base area of the triangular prism:
base area = (1/2) * base * height = (1/2) * 27.9cm * 5.1cm = 71.145cm
Next, let's calculate the base perimeter:
base perimeter = 28.4cm + 27.9cm + sqrt((28.4cm)^2 + (27.9cm)^2)
base perimeter = 28.4cm + 27.9cm + sqrt(807.36cm^2 + 780.41cm^2)
base perimeter = 28.4cm + 27.9cm + sqrt(1587.77cm^2)
base perimeter = 28.4cm + 27.9cm + 39.843cm
base perimeter = 96.143cm
Now we can calculate the surface area of the triangular prism:
SA = (2 * 71.145cm) + (96.143cm * 5.1cm)
SA = 142.29cm + 489.639cm
SA = 631.929cm
Therefore, approximately 632 square centimeters of wrapping paper are needed to wrap the toy.