Square Footage of a Triangle
Area of a triangular space from its base and its perpendicular height — the shape a gable end makes, or a corner of a room where nothing is square.
A triangular area needs the perpendicular height, not the length of a sloping side. On a gable at a 6/12 pitch the slope runs about 12% longer than the height, so measuring up the rafter overstates the area by the same 12% before anything else goes wrong.
With base 12 ft, height 8 ft, number of identical areas 1, waste factor 10 percent and 1 more field, square footage comes to 52.8 sq ft — area to order. It is reached in 9 steps, the last of which is 48 * (1 + 10 / 100), and each one is printed on the page with its numbers filled in. The formula is the one published by ANSI Z765 residential square footage measurement standard, not an approximation fitted to it.
Formula and sources checked · How we check
- The three sides close into a triangle
1- Area of the openings
2 * 3 * 530 sq ft- Area per shape
48 sq ft- Total area
48 * 148 sq ft- Area to order
48 * (1 + 10 / 100)52.8 sq ft- Same area in square meters
52.8 * 0.0929034.905 sq m- Same area in square yards
52.8 / 95.867 sq yd- Same area in acres
52.8 / 435600.001 acres- Material at that price
52.8 * 0$0
Several at once
A job is rarely one of anything. Work out the first, add it, change the figures and add the next — the list keeps what each line was, and totals them.
Which measurement is the height?
The perpendicular distance from the base to the opposite corner, taken square to the base. On any triangle that is not right-angled that line falls inside the shape rather than along an edge, which is exactly why a tape run up a sloping side returns a figure that is too large.
What if you can only measure the three sides?
Heron’s formula needs no height at all: take half the perimeter, subtract each side from it in turn, multiply the four numbers together and take the square root. It is the method for a corner of a room where every side can be reached and no height can.
The formula
- The three sides close into a triangle
heron > 0 ? 1 : 0 - Area of the openings
openings * opening_w * opening_h - Area per shape
shape_rect * (length * width) + shape_wall * max(0, length * width - openings_area) + shape_border * ((length + 2 * border_width) * (width + 2 * border_width) - length * width) + shape_trapezoid * ((top_width + bottom_width) / 2 * trap_height) + shape_circle * (pi * pow(diameter / 2, 2)) + shape_annulus * (pi * (pow(diameter / 2, 2) - pow(min(inner_diameter, diameter) / 2, 2))) + shape_triangle * (base * tri_height / 2) + shape_triangle_sides * sqrt(heron) - Total area
area * rooms - Area to order
subtotal * (1 + waste / 100) - Same area in square meters
total * 0.09290304 - Same area in square yards
total / 9 - Same area in acres
total / 43560 - Material at that price
total * price
Formula from ANSI Z765 residential square footage measurement standard, NIST Office of Weights and Measures.
The same calculator, other cases
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