Use the image to answer the question.
An illustration shows an unfolded version of a triangular prism.
There are 3 horizontal rectangles stacked on top of one another. The first and the last are similar and the middle one is larger. The horizontal length of the three rectangles is 20 centimeters. The vertical width of the second rectangle is 16 centimeters. There are two similar triangles adjoined to the left and right of the second rectangle, with the rectangle width as the triangle bases. The perpendicular length of the triangle, drawn as a dotted line from the top vertex to the middle of the base, is 6 centimeters; it is denoted by a right angle symbol. The length of the hypotenuse slant is 10 centimeters. All interior lines are drawn as dashed lines, and all outer lines are solid.
Chocolate Bliss makes a candy bar in the shape of a triangular prism. The prism is represented by the net given. For packaging, the top and bottom are covered in gold foil, and the faces are covered in red foil. How many cm2 of red foil are needed for one candy bar?
(1 point)
Responses
960 cm2
960 cm squared
720 cm2
720 cm squared
1,056 cm2
1,056 cm squared
816 cm2
To find the total surface area of the candy bar, we need to calculate the area of all the faces. The triangular faces have an area of (1/2) x base x height. Since the base is 20 cm and the height is 16 cm, the area of each triangle face is (1/2) x 20 x 16 = 160 cm2.
Since there are two triangular faces, the total area for both triangles is 160 cm2 x 2 = 320 cm2.
The rectangular faces have an area of width x height. Since each rectangle has a width of 20 cm and a height of 16 cm, the area of each rectangle face is 20 cm x 16 cm = 320 cm2.
Since there are three rectangle faces, the total area for all three rectangles is 320 cm2 x 3 = 960 cm2.
Adding the areas of the triangular and rectangular faces together, the total red foil needed for one candy bar is 320 cm2 + 960 cm2 = 1,280 cm2.