# Triangular prism on top of rectangular prism in the shape of a house.....

#### Sting124

##### New member
What formula would you use to calculate the area (excluding the base)?

What formula would you use to calculate the volume?

What would its longest side be?

#### MarkFL

Staff member
Re: triangular prism on top of rectangular prism in the shape of a house.....

Do you have any information regarding the dimensions?

edit: I recently was giving a student help on a practice worksheet containing 11 problems, and this was essentially problem 10, but a diagram was missing and the question unanswerable. Are you perhaps working on the same set of practice problems?

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#### Sting124

##### New member
Re: triangular prism on top of rectangular prism in the shape of a house.....

Yes, he is the one who pointed me towards this website unfortunately this image was missing as you know, but there may be a chance to retrieve it.

#### Klaas van Aarsen

##### MHB Seeker
Staff member
Re: triangular prism on top of rectangular prism in the shape of a house.....

If it is the shape of a house, it should still be doable.

We'd have a house with say length L and width W.
The block part of the house can have height H.
And the roof part can have height h for a total height of (H+h).

Then you'd have to calculate how much area the walls and roof have.

#### Sting124

##### New member
Re: triangular prism on top of rectangular prism in the shape of a house.....

The slant heights are already in the question I provided for you

- slant heights 15m
- length = 48m
- Width = 24m
- height = 32m

Mark could you help my sibling over at the other forum for question 10 if not help me here please

#### Sting124

##### New member

Shape of a house, triangular prism on top a rectangular prism

- Slant heights 15m
- length = 48m
- Width = 24m
- height = 32m

What is the area (excluding the base)?

What is the volume?

If a scale model was made with the longest side being 2m in length. What would the volume of scale model to actual model as a ratio be.

#### Klaas van Aarsen

##### MHB Seeker
Staff member
Re: triangular prism on top of rectangular prism in the shape of a house.....

The slant heights are already in the question I provided for you

- slant heights 15m
- length = 48m
- Width = 24m
- height = 32m

Mark could you help my sibling over at the other forum for question 10 if not help me here please
Well, a house consists of 4 rectangular walls, 2 rectangular roof parts, and 2 triangular wall sections that are part of the roof.

The area of a rectangle is length x width.
The area of a triangle is base x height / 2.

Can you find the total area with this?

#### MarkFL

Staff member
Re: triangular prism on top of rectangular prism in the shape of a house.....

...
Mark could you help my sibling over at the other forum for question 10 if not help me here please
I just sent a PM at the other forum.

The total area consists of 6 rectangles and 2 triangles. All measures are in meters.

There are 4 vertical rectangles making up the outer wall of the rectangular prism, 2 of these are 24 X 32 and two are 48 X 32.

There are two rectangles making up the roof, and they are 15 X 48.

There are two triangles at each end of the roof, whose height $h$ may be found using the Pythagorean theorem:

$$\displaystyle 12^2+h^2=15^2$$

Once you find $h$ then the 2 triangles have a combined area of:

$$\displaystyle A=2\left(\frac{1}{2}\cdot24h \right)=24h$$

This should allow you to find the area. Now as for the model, its longest side is 2, and the longest side of the actual shed is 48 so the scale of the mode is 1:24. When the linear measure of a 3 dimensional solid is multiplied by some factor $k$, the ratio of the volume of the original to the volume of the scaled version is then $$\displaystyle \frac{1}{k^3}$$. So, what would the ratio be in this case?

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