An illustration shows an unfolded version of a triangular prism.

Question

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?

Answer 1

To calculate the surface area of the candy bar covered in red foil, we need to find the area of each face and add them together.

The first and last faces are rectangles with dimensions 20 cm by 16 cm, so the area of each of these faces is:
Area = length x width
Area = 20 cm x 16 cm
Area = 320 cm^2 (for each face)

The middle face is a triangle with a base of 20 cm and a height of 6 cm. The area of a triangle is:
Area = 1/2 x base x height
Area = 1/2 x 20 cm x 6 cm
Area = 60 cm^2

Now, add the areas of all three faces together to get the total surface area covered in red foil:
Total area = 2(320 cm^2) + 60 cm^2
Total area = 640 cm^2 + 60 cm^2
Total area = 700 cm^2

Therefore, Chocolate Bliss would need 700 cm^2 of red foil for one candy bar.

Answer 2

A “wet floor” warning sign is in the shape of a triangular pyramid without a base. The edge length of the base equilateral triangle is 15 inches, the height of the base triangle is 13 inches, and the height of the triangular faces is 18 inches. How much fabric is needed to make the sign given the base does not need fabric?

Answer 3

To calculate the surface area of the triangular pyramid that needs fabric, we need to find the area of each triangular face and add them together.

First, let's calculate the area of the triangular faces. The area of an equilateral triangle can be calculated using the formula:
Area = (sqrt(3)/4) x (side length)^2

For the base triangle:
Area_base = (sqrt(3)/4) x 15^2
Area_base = (sqrt(3)/4) x 225
Area_base = 56.25 sqrt(3) square inches

Now, let's calculate the area of one of the triangular faces with height 18 inches:
Area_face = (1/2) x base x height
Area_face = (1/2) x 15 x 18
Area_face = 135 square inches

Since the pyramid has 3 identical triangular faces, we can now calculate the total fabric needed for the 3 faces:
Total fabric = 3 x Area_face
Total fabric = 3 x 135 square inches
Total fabric = 405 square inches

So, 405 square inches of fabric are needed to make the wet floor sign with the triangular pyramid shape.