Triangle Square Footage Calculator
Enter the base and perpendicular height of any triangle. The calculator returns the area using the
formula (base × height) / 2 — works for every type of triangle.
Tip: If you only have the diameter, divide by 2 to get the radius.
L-shape = two rectangles sharing a corner.
Add one row per rectangle and we'll sum them.
Triangle Area Formula
The classic formula is Area = (base × height) / 2, where height is the perpendicular
distance from the base to the opposite vertex, not the length of the other side.
- Base 10 ft, Height 8 ft → (10 × 8) / 2 = 40 sq ft
- Base 14 ft, Height 9 ft → (14 × 9) / 2 = 63 sq ft
- Base 20 ft, Height 15 ft → (20 × 15) / 2 = 150 sq ft
Finding the Height of a Triangle
For a right triangle, the two legs meeting at the right angle are the base and height. Otherwise, measure the perpendicular distance from the opposite vertex to the base line. For an obtuse triangle, extend that line beyond the side if necessary; the perpendicular can land outside the triangle.
For a triangular gable wall, use its horizontal base and vertical rise to the peak. A sloping edge is not the height. Roof-surface measurements lie in the roof plane; do not substitute a wall's vertical rise or a horizontal plan-view dimension.
Gable Wall: Check the Window Fit Before Deducting Its Area
Suppose a flat, symmetric triangular gable wall has a 20 ft horizontal base and an 8 ft vertical rise, with the peak above the base midpoint. A rectangular window opening is 3 ft wide and 4 ft high, horizontally centered beneath the peak. Its sill is 1 ft above the triangle's baseline, so its top is 1 + 4 = 5 ft above that line. These are opening dimensions for the excluded wall face, not nominal window product dimensions.
| Step | Calculation | Result |
|---|---|---|
| Gross triangular wall area | (20 × 8) / 2 | 80 sq ft |
| Wall width at the window top | 20 × (1 − 5/8) | 7.5 ft |
| Window opening area | 3 × 4 | 12 sq ft |
| Net wall face area | 80 − 12 | 68 sq ft |
By similar triangles, the available width narrows with height. At the opening's top, the centered 3 ft width fits inside 7.5 ft, leaving (7.5 − 3) / 2 = 2.25 ft on each side. The wall is wider below that level, and the sill is above the baseline, so the entire rectangle fits inside the triangle. Only then can we deduct all 12 sq ft; for an opening crossing the boundary, deduct only the portion inside the measured face.
Each slanted gable edge is √(10² + 8²) ≈ 12.806 ft. That is a side length, not the 8 ft perpendicular height used to calculate the wall area.
What 68 sq ft means: net vertical wall face area, not roof area or attic-floor area. These wall dimensions do not determine the separate sloping roof surfaces or the horizontal floor plan. It is also not a siding purchase quantity: layout, cuts, trim, waste, and manufacturer instructions still matter. The fit check is geometry, not structural framing approval. Use dimensions from plans or measurements obtained with safe access; do not climb onto a roof to obtain them.
Obtuse Triangle: Extend the Base Line, Not the Base Length
Consider a flat triangle with coordinates in feet: A = (0, 0), B = (12, 0), and C = (−3, 4). Choose AB as the base. The perpendicular from C meets the extended base line at D = (−3, 0), 3 ft beyond A, outside the triangle.
| Measurement | Length | How to use it |
|---|---|---|
| Original base AB | 12 ft | Keep this as the base. |
| Perpendicular CD | 4 ft | This is the height. |
| Sloping side AC | 5 ft | A side, not the height. |
| Extended distance DB | 15 ft | Only for the enclosing-triangle cross-check. |
If the 5 ft side and 3 ft offset are known, the perpendicular height is √(5² − 3²) = 4 ft. Using the original base, the area is (12 × 4) / 2 = 24 sq ft.
Check the result by subtracting the small exterior right triangle ADC from the enclosing right triangle DBC: (15 × 4) / 2 − (3 × 4) / 2 = 30 − 6 = 24 sq ft.
The base remains 12 ft, not 15 ft. Extending the base line only locates the perpendicular foot. Using either the extended 15 ft distance as the base or the sloping 5 ft side as the height would incorrectly give 30 sq ft.
Common Uses for Triangle Square Footage
- Gable walls — calculate the triangular portion above the rectangular wall, then deduct openings that lie within it.
- Triangular floor sections — use dimensions measured in the floor plane. A triangular attic cross-section does not mean the attic floor is triangular.
- Garden beds — area can estimate sod coverage; mulch volume also needs depth.
- Roofing — measure each triangular section in the sloping roof plane, not from a gable elevation.
Frequently Asked Questions
How do I calculate the square footage of a triangle?
Multiply the base by the perpendicular height and divide by 2. A 14 ft × 9 ft triangle is (14 × 9) / 2 = 63 sq ft.
What if I don't know the perpendicular height?
For a right triangle, choose one leg as the base and the other as the height. For other triangles, measure perpendicular to the chosen base line from the opposite vertex, extending the line as needed. The perpendicular can land outside the triangle, as in the obtuse example; it need not point vertically down the page. If you know only the three side lengths, use Heron's formula separately. This calculator requires a base and perpendicular height, not three side inputs.
Does this formula work for scalene and isosceles triangles?
Yes. As long as you use the perpendicular height (not the slant length), (base × height) / 2 works for every triangle.
Geometry References
Math Open Reference explains the perpendicular altitude, including an extended base line and the half-base-times-height area formula. These references support the geometry rules; the numerical examples and window-fit check above are our own calculations, not examples or construction approvals supplied by those sources.