Im ! a pencil holder shaped like a triangular prism has a height of 3 in and volume of 16.5in squared. what is the area of the triangular prism in square inches ( explain the way to do this fully as i have no idea how to do this on my own and yes this is the full question)

5.5 in^2

Step-by-step explanation:

The volume of any sort of prism is given by the formula ...

V = Bh

where B is the area of the base ahd h is the height. Fill in the given information and solve for the unknown variable:

16.5 in^3 = B·3 in

(16.5 in^3)/(3 in) = B = 5.5 in^2 . . . . . . divide by the coefficient of B

The area of the base is 5.5 square inches.

Comment on the working

I like to keep the units with the numbers to make sure I'm doing the math correctly. If the untis come out wrong, then I've set up the problem wrong. They multiply and divide the same way any variable does:

in^3 / in = in^2

The volume will be measured in cubic inches; the area will be measured in square inches.

think the answer would beb

18 units²

step-by-step explanation:

first let's find altitude bd using the distance formula

d = √((y₂ - y₁)² + (x₂ - x₁)²)

bd = √((0 - -3)² + (0 - 3)²)

bd = √18

given the placement of points a and c, we can denote that point d bisects segment ac.

we will call ac the base.

using the distance formula

ac = √((0 - 6)² + (-6 - 0)²)

ac = √72

knowing our base and our height, we can plug these into our triangle area formula

area = (b * h)/2

area = (√18 * √72) / 2

area = (√1296) / 2

area = 36 / 2

area = 18 units²