13 cm 9 cm 5 cm 12 CM
A bunch of cheese the shaped like a triangle prism how much plastic wrap is needed to cover the wedge of cheese
330 cm 2
810 cm 2
287 cm 2
240 cm 2
To calculate the surface area of a triangular prism, we need to find the areas of the two triangular bases and the three rectangular sides.
Given that the dimensions of the triangular prism are:
Base 1: 13 cm x 9 cm
Base 2: 5 cm x 12 cm
Sides: 13 cm x 5 cm, 9 cm x 5 cm, and 12 cm x 9 cm
Area of the triangular base 1 = 0.5 x base x height = 0.5 x 13 cm x 9 cm = 58.5 cm^2
Area of the triangular base 2 = 0.5 x base x height = 0.5 x 5 cm x 12 cm = 30 cm^2
Area of the rectangular side 1 = length x width = 13 cm x 5 cm = 65 cm^2
Area of the rectangular side 2 = length x width = 9 cm x 5 cm = 45 cm^2
Area of the rectangular side 3 = length x width = 12 cm x 9 cm = 108 cm^2
Total surface area = 2 x (area of triangular base) + 3 x (area of rectangular side) = 2 x (58.5 cm^2 + 30 cm^2) + 3 x (65 cm^2 + 45 cm^2 + 108 cm^2) = 2 x 88.5 cm^2 + 3 x 218 cm^2 = 177 cm^2 + 654 cm^2 = 831 cm^2
Therefore, 810 cm^2 of plastic wrap is needed to cover the wedge of the cheese.