Question

A garden post is in the shape of a square prism with a square pyramid on top. A butterfly is flying around and lands on the post. Note: The diagram is not drawn to scale.

A triangular prism of height 6 inches. on top of a cuboid of height 5 ft and breadth 4 inches


Complete each part of this task to determine the probability the butterfly lands on a specific part of the post.


Part A

What is the surface area of the garden post that the butterfly could land on, to the nearest square inch? Show your work.

Answer 1

The garden post consists of two parts: a square prism and a square pyramid.

The surface area of the square prism is 4(side)^2, where side is the length of one of the sides of the square base. Since the triangular prism on top of the cuboid has the same base as the square prism, the side of the square base is 4 inches. So, the surface area of the square prism is:

4(4)^2 = 64 square inches.

The surface area of the square pyramid is given by the formula:

base area + 1/2 * perimeter of base * slant height

The base area of the pyramid is (side)^2, where side is the length of one of the sides of the square base. The perimeter of the base is 4*side, and the slant height is given as 6 inches. So, the surface area of the square pyramid is:

4^2 + 1/2 * 4*4*6 = 16 + 48 = 64 square inches.

Therefore, the total surface area of the garden post that the butterfly could land on is:

64 + 64 = 128 square inches.