Dream House Project

In Geometry class, my group and I have completed the first part of the Dream House Project. It is a fun project. We were given $1,000,000 to buy a piece of land, and design a dream house. With continuous support each other, our group members have not only designed the floor plan of our house, but we have also calculated the cost of all the building materials that would be necessary to build the house. Our "house" is located at a 5,000 sq. foot lot in Richmond, California.

Here is a copy of a five-page paper written by my friend which goes into detail about our house. This is not my work at all, but is solely written by him. I have not mentioned his name for privacy.

Over the course of human history, technology has changed and our lifestyle has evolved. However, one of the things that have remained constant is our ingenuity, which we have employed to build advanced shelters known as houses. Nowadays, with the advent of currency and the real estate industry, most people have obtained their house by buying it. However, it is becoming an increasingly popular alternative in our modern culture to build houses ourselves as we once did and only buy land, materials, and labor for them. In our project, we basically had find land in the Bay Area that cost less then $100,000 where we could build our house. We then had to use the rest of our $1,000,000 budget and "spend" it on all the materials and labor we had to use to build our own dream house from the ground up. In the project, we first had to pay a base cost of $175 for every square foot of every room in the house. Our house also needed to have a kitchen, bedroom, bathroom, and living room. Now, as I've implied, we did have to pay for the land. In fact, our land in Richmond, California (north of Berkeley) cost us $80,000. In our model, the scale will most likely be 1cm:2ft. Anyway, before I can talk about that however, I need to discuss what area is. I will do that in the following section.

So, at its most basic definition, area is simply length times width. However, it stretches far beyond that. Now, if our floor plan and plots of land on Earth were one dimensional like a line, area would simply be that same as the length of the line, as this is the amount of space the line takes up due to the fact that length is the only dimension in a one dimensional scenario. In a three dimensional world like the one we live in, objects don't simply have length but also width and height, as these are three dimensions. Thus, area in a three dimensional world is length times width times height; also known as volume. Now, when people use the word area in a mathematical sense, they are referring to the area of two dimensional objects. Now, in two dimensions, objects have length and width, but nor height as they lie in a flat plane. This is why area equals length times width. Now, even though we live in a three dimensional world, we still use area sometimes when referring to he sizes of two dimensional objects within our three dimensional world such as two dimensional shapes and even plots of land. Now, when measuring one dimensional area, better known as length, we use length units such as meters, feet, cm, in., etc. When measuring regular area, basically that of two dimensional objects we use square units such as square cm, square in., square feet, etc. Similarly, when messing three dimensional area, also known as volume, we measure in cubic units such as cubic feet, cubic cm, etc. Now, let's use one of the rooms in our dream house floor plan as an example of how to measure area. For our garage, the width is fifteen feet. The length is twenty feet. So, to find area, we must multiply this room's length by its width. So, the area of the garage, g, is the product of the length, L, and width, W. So, G = L * W. We can substitute in our values to get G = 20 * 15. Of course, with some multiplication, we can simplify this to get G = 300. Hence, the area of our house's garage is 300 square feet. Simple, right? Well, in the next section, we'll do some more examples like this just to get the full sense of how to calculate area. We'll also use the area to find the base cost of the room when we factor in the $175 price for every square foot.

So, for our first example, let's take our family area. Now, we'll represent the total area of this room with the variable F. The length of this room, not including the walls, is 29 ft. We'll represent that as the variable L. The width of the room is 25 feet. We'll represent that as the variable W. So, using the area formula of area = length * width, we can insert in our variables. This gives us the formula F = W * L. If we substitute in our length, 29 feet; as well as our width, 25 feet, we are left with the equation, F = 29 * 25. If we evaluate for like terms in this equation, we get the equation, F = 725. Thus, we can conclude that the area of the family area is 725 square feet. However, we still don't know the cost of the room when we factor in the base cost I mentioned earlier. However, now that we know that area, we can find that easily. You see, the base cost is $175 per square foot. Our area is already measured in square feet, which means that in order to find the base cost, B, of the family area, we simply need to multiply the area of the room in square feet, F, by 175. This gives us the equation B = 175 * F. If we substitute in our value for the family room area which we calculated already, we get the equation B = 175 * 725. If we evaluate the like terms in this equation, we get the equation B = 126,825. Hence, the base cost of the family room is $126,825. Simple,right? Well then, let's try it with the guest bathroom. The length of our house's guest bathroom, L, is 10 feet. It's width, W, is also 10 feet. This means that our guest bathroom is a square, as it has equal length and width. Now, when you're dealing with the area of a square, instead of using the formula I mentioned earlier, you can simplify things and use this formula: Area = (side length) ^ 2. Just in case y didn't know, that little sign is a power sign. So, this equation reads as "area equals side length to the power of two." Basically, the area of our guest bathroom, V, is the side length, S, squared. We can write this out as V = S ^ 2. When we substitute the values, we get V = 10 ^ 2, which can be simplified as V = 100. Now, to find the base cost, B, we just multiply 175 by the area, V. This gives us the equation, B = V * 175. When we plug in our values, we get B = 100 * 175, which gives us the simplified equation, B = 17,500. Hence, the base cost of the guest bedroom is $17,500.

Our rooms do have reasonable areas. This is because of the following reasons. First of all, here's why our master bedrooms, which are 20x10 are suitable areas for a bedroom. First of all, our bedrooms do have enough space for a queen bedroom each, which in fact, measure no more then 6x7 feet. This gives us more then enough room to put other furnishings such as a dresser and desk in all the room while maintaining comfort. In addition, our master bathrooms, which are each 9x9.75, are of appropriate dimensions as well. This gives us more then enough space for a toilet, shower, and sink with space to spare. Anyway, let's look at the dimensions of the family area. The family area is 20x30 feet. As you can see here, this gives us a very spacious yet not unfathomably massive space to relax.

In this section, we shall detail to you the dimensions, floor plan, and monetary situation of our house.The area of our property is 5148 square feet, with a length of approx. 101 square feet, and a width of approx. 50 feet. Out of this amount, 2458 square feet is taken up by our house, whose dimensions are 65 by 45 feet. Anyway, let's talk about perimeter. The perimeter of our property is approx. 302 feet. Meanwhile, the perimeter of our house is approx. 201 feet. Moving along, let's discuss our budget. Out of our $1,000,000 budget, we spent about $580,588 on our house construction, flooring, landscaping, and other necessities. This leaves us with about $419,413 left in our budget. The reason for this huge amount of money left is due to the extensive deal hunting our group engaged in to keep costs as low as possible. Now, regarding this leftover money, we plan to use it on stuff such as furniture, appliances, and amenities (i.e. Gaming computer, ping pong table, etc.). Finally, let's discuss our room data and floor plan. When one first enters the house via the front door, he or she finds himself in the kitchen and dining area. Now, this isn't a distinct room. Instead, it's an area leads into the family area (which also functions as Nathan's room), which is east of the dining/kitchen area of the entire combined room area. To the north of the front door is the garage. Also, to the southeast of the kitchen and southwest of the family area is the guest bathroom for when visitors come to our house. To the east of the family room are 2 master bedrooms and 2 master bathrooms. Anyway, for more information about both the room data and budget update, please refer to the photos of our floor plan and budget sheet, which can be found on the next few pages.

Here are the general restrictions of our project:

• Land has to be in the Bay Area
• Land has to cost $100,000 or less
• The cost of everything combined has to be one million dollars or less
• House has to have normal rooms (ex: kitchen, bathroom, bedroom), but may have special rooms (ex: indoor theater)
• Building cost and materials have to be included in the budget

Here are some pictures of the floor plan of our house: