Calculating the Area of a Complex Roof
Areas of complex roofs with multiple hips and valleys take the most time to calculate. Start by making a rough sketch of the roof. To simplify the calculation, break down the sketch into rectangles and right triangles (triangles with one 90-degree corner), then take as many measurements of the roof as you can to match the sides of the rectangles and triangles on the sketch.
Use visual cues from the existing roof shingles or roof sheathing to determine square lines off eaves edges or ridges. These cues will help you measure the lengths of the sides of the rectangles and triangles. For instance, the cutout slots on shingled roofs run perpendicular (90 degrees) to the eaves, and nail rows in sheathing are pretty close to square also. It is difficult sometimes to get accurate measurements. Don’t get too concerned though; just round lengths to the nearest 6 in.
With the sketch filled in with measurements, you can determine the size of the roof area. The area of a rectangle is length multiplied by width, whereas the area of a right triangle is the length of the two sides that meet at the 90-degree corner multiplied together and divided by two (this works because a right triangle is half a rectangle).
Tally the square footages of all the rectangles and triangles, which will give you the total square footage for the roof. The example here shows the calculation for a roof with two hips.