How can I calculate the area of a weirdly shaped house some corners not 90 degrees and it has a wall that's curved?

Answer 1

What you are actually trying to do is calculate the area of an irregular polygon (excluding the curved wall). One way to do that is to use coordinate geometry (see link in Related Links) to give each corner of the house an x/y set of values and then put the measurements of each wall on a paper over an x/y coordinate system.

So first you need to draw up a floor plan of your house. Then you'd start of with one corner of the house and say that's the 0/0 positions. Draw a line starting from that corner along one of the walls that starts from that corner (x-axis) and then draw another line that's at a 90 degree angle (y-axis). The 2 lines represent the coordinate system. You need to measure the length of the wall over which you drew the first line and divide the x-axis into 1-foot increments and mirror that on the y-axis. Once you have that, you can assign x/y coordinates to each corner of the house.

With those coordinates you calculate this sum:

(x1y2 - y1x2) + (x2y3 - y2x3) + ... + (xny1 - ynx1)

Dividing the sum by 2 gives you the area of the house (in square feet).

The part of the house that contains a curved wall needs to be calculated separately and added to the area calculated above. This is a bit more complicated. Assuming that the curved wall can be considered part of an imaginary circle (so it's a regular curve), what you're actually doing is calculating the area of a segment of a circle.

On the floor plan you drew in the first step, draw a circle that traces over the curved wall and highlight the center of the circle and the 2 'corners' of the curved wall on the circle. The area between these 3 points is the area of a segment of a circle. The radius of the circle is the distance between the center and one of the wall corners (which you can figure out using the x/y coordinate system you drew). You also need to measure the angle between the 2 lines connecting the center and the 2 corners. Once you have these values, calculate the area of the segment using the formula: A = PI * r2 * angle/360. Now calculate the area of the triangle between the 3 points by using the formula you used in the first step (coordinate system). If you substract the area of the triangle from A, you get the area of the segment which you can add to the area you calculated in step 1 to result in the total area of the house.

This is quite a bit of work, indeed, but if you can manage to draw the floorplan of your house, you can always use an online area calculator that does the calculations for you. Once such tool is linked in the Related Links.