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.
@botttt
To find the total surface area of the triangular prism, we need to calculate the area of each of its faces.
1. Base: The area of the base is the area of the right triangle.
Area = 0.5 * base * height
= 0.5 * 27.9 * 5.1
= 71.145 square centimeters
2. Top: The area of the top face is the same as the base.
Area = 71.145 square centimeters
3. Front and back faces: The front and back faces are also right triangles, so we calculate the area using the same formula.
Area = 0.5 * base * height
= 0.5 * 30.5 * 5.1
= 77.775 square centimeters
4. Left and right faces: The left and right faces are rectangles. The area of a rectangle is given by:
Area = length * height
= 30.5 * 28.4
= 866.2 square centimeters
Now, we add up all the areas to find the total surface area of the triangular prism:
Total surface area = 2 (base area) + 2 (front face area) + 2 (left/right face area)
= 2(71.145) + 2(77.775) + 2(866.2)
= 142.29 + 155.55 + 1732.4
= 2030.24 square centimeters
Therefore, approximately 2030 square centimeters of wrapping paper is needed to wrap the toy.