Question

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Teacher gives us answers but we have to show work

Having trouble with this one

Answer 1

@mathstudent55

Answer 2

Do you know what a prism is?

Answer 3

Yes!

Answer 4

The greenhouse is shaped like a prism.
You need to find the volume of the prism.

Answer 5

For this greenhouse, the front and back faces are pentagons.
They are the bases of the prism.
The height of the prism is the distance between the bases, or 35 m.

Answer 6

To find the volume of a prism, multiply the area of the base by the height.

Answer 7

We need the area of the base.

Answer 8

So, I multiple 14x the area of the pentagon?

Answer 9

This is the pentagon.
We need its area.
Once we have the area of the pentagon, then since the pentagon is the base of the prism, we multiply the area of the pentagonal base by the height of the prism to find the volume of the prism.

Answer 10

You multiply the area of the pentagon by 35 m because 35 m is the height of the prism.

Answer 11

Let's go back to the pentagon and figure out its area.

Answer 12

Height of the prism?

Answer 13

Alright, how do we do so?

Answer 14

One way of finding the area of a complex figure is to break it up into simpler figures.
Our pentagon can be broken up into a rectangle and a triangle.

Answer 15

The rectangle part has dimensions 14 ft by 8 ft.
What is the area of the rectangle?

Answer 16

112

Answer 17

Good.
Now we need to deal with the triangle.
We need a base and a height.
The 14 ft side is the base.
We need to calculate the height.

Answer 18

Pythag theorem=7.14.

Answer 19

@mathstudent55

Answer 20

Excellent work.

Answer 21

Now you can find the area of the triangle since you have the base (14 ft) and the height (7.14 ft).

Answer 22

24.98

Answer 23

49.98*

Answer 24

Which means 49.98+112=base of our area right?

Answer 25

161.98 right?

Answer 26

Good.
Now add the area of the triangle to the area of the rectangle to have the area of the pentagonal base.

Answer 27

Correct.

Answer 28

Now times this by 35?

Answer 29

Now that you have the area of the base, multiply it by the height of the prism to find the volume of the prism.

Answer 30

Yes.

Answer 31

5,669.3

Answer 32

Here is a piece of advice.
When you calculate, keep the numbers in the calculator without rounding off.
Do all the calculations.
Then round off only at the end the final answer.
Doing it this way, I get 5669.649965 which rounds off to 5669.6.
The answer is 5669.6 ft^3 since it's a volume.

Answer 33

Alright! What's next?

Answer 34

Oh wait nvm that's the answer haha

Answer 35

This problem's done.