math at home?

Question

im building a bird house with a pitched roof and need to know how to get the measurement to the middle of the roof. it will have 1 point in the middle of the roof the sides going up will be triangular

Answer 1

If by "measurement" you mean the actual distance from the peak, to the edge....

Assuming the roof line looks like the letter "A" -

This can be answered by looking at the 'end' of the bird house. Find the distance from the peak to the horizontal line that would run from one roof edge, to the opposite one. Call this measurement "A".
Now, measure the distance along that line from roof edge to the opposite roof edge, and divide it by 2. Call this number "B".
What you've got now, is two side lengths of two seperate right angle triangles. (the right angle being at the location where the 'vertical' measurement "A", intersects with the horizontal measurement of roof edge to roof edge, which we have named "B".

Using the simple math formula now of Pythagorus Theorum, A-squared Plus B-Squared Equals C-Squared. "C" is the length of the roof from peak, to edge.

An example -- Lets say you are building a BIG birdhouse.....and the measurement of peak to horizontal is 3 feet. The measurement of roof edge to roof edge equals 8 feet (remember to divide this in half) making "B" equal 4 feet.
A-Squared (3 times 3 equals 9 feet) Plus
B-Squared (4 times 4 equals 16 feet) Equals
C-Squared (9 plus 16 equals 25, the square root of which is 5)
This would mean that the distance from the roof peak to edge would be 5 feet.

This ancient math formula can be used with any pitch roof...it doesnt matter how "high" the peak is. By creating the imaginary 2 right angle triangles, you can easily calculate the distance of the 'hypotenuse', or in this case, the distance from the peak to the edge of the roof.

If the roof line is peaked like an egyptian pyramid, then you simply keep dividing the roof line into as many triangles as you need, to find that 'long edge' of the right triangle. Once you know the distance from the peak to the edge, you can then divide that roof section into 2 triangles, and calculate the distance along the "corner" of the pyramid.

Have Fun