Question

Lyle sliced a block of cheese along a diagonal into two triangular prisms as shown. Lyle says that the surface area of the block is 2 times the surface area of one of the triangular prisms. Do you agree? Explain your answer This is followed by: Refer to problem 5. Find the difference between the surface area of the two triangular prisms and the surface area of the surface area of the rectangular prism. Show your work. Help now plz!!!

Answer 1

Explanation:

I have attached an image to make question clearer.

(A) Yes, the surface area of the block is twice the surface area of one of the triangular prisms. This is because the block has opposite faces to be equal since it's a cuboid, also all it's faces to be made of rectangles, therefore cutting it from the diagonal makes two equal triangles. Hence, the two triangular prisms are the same and since they are the same, two of the prisms will make up the block again. In conclusion, the surface area of the block will be times two of one of the triangular prism's surface area.

(B) since the surface area of the block is times two of the surface area of the triangular prism. Then we should look for the area of the prism.

Surface area of cuboid is given as:

2(L x W + L x H + W x H)

L = 4.5, W = 3 and H = 4.

Surface area = 2(4.5*3 + 4.5*4 + 3*4) = 87

Since the surface area is 87, then the surface area of one of the two triangles will be

87/2 = 43.5.