1. Tyler bought a pencil holder in the shape of a triangle prism, as a gag gift for his friend’s birthday

Question

1a) He fills the pencil holder with sand before he wraps it to make it feel like a heavy, expensive gift. How much sand will he need to “borrow” from his sister’s sandbox to fill the pencil holder?
a) 21 cubic inches
b) 7.5 cubic inches
c) 9.375 cubic inches
d) 10.5

Answer 1

the volume is the base area times the height.
You have supplied neither of those.

I assume you know how to find the area of a triangle ...

Answer 2

obviously lmao it’s height time base divided by 2

Answer 3

What is the minimum amount of saran wrap that Tyler will need to cover the pencil holder, to ensure that no sand leaks out?

a) 11.75i * n ^ 2

b) 13.5i * n ^ 2

c) 14.75i * n ^ 2

d) 32.25i * n ^ 2

e) 34i * n ^ 2

Answer 4

We need to find the surface area of the triangular prism which is the sum of the areas of the three rectangular faces.

Let's assume that the triangle has base "b" and height "h", and that the prism has a height of "n" inches.

The area of the rectangular face that has a base of "b" and a height of "n" is:

b * n

The other two rectangular faces will have a base of "h" and a height of "n". To find their areas, we need to first find the slant height of the triangle, which is:

sqrt(b^2 + h^2)

Then, using the slant height "s", we can find the height of those rectangular faces using the Pythagorean theorem:

sqrt(s^2 - h^2)

The area of each of those rectangular faces is then:

h * sqrt(s^2 - h^2)

So, the total surface area is:

b * n + 2h * sqrt(s^2 - h^2)

Plugging in the values we know:

b = ? (not given)

h = height of triangle = ? (not given)

s = slant height of triangle = ? (not given)

n = height of prism = ?

We cannot determine the surface area without knowing the length of at least one side of the triangle. So, none of the given answer choices are correct.