Triangle Square Footage Calculator — Area Using Base & Height or All Three Sides
Triangular areas appear more often in construction and landscaping than most people expect. Hip roof sections, corner garden beds, triangular patio corners, gable end walls, sail-shade anchoring areas, and sloped site drainage zones all require triangle area calculation. The calculator supports two methods: base-and-height (when you can measure the perpendicular height) and Heron's formula (when you can only measure the three sides directly).
Use the base-and-height method for right triangles and any triangle where the perpendicular height is accessible. Use Heron's formula for triangles measured directly on the ground, such as a corner lot boundary or a triangular island bed where you can walk the perimeter but not the height.
Base and Height Method
Formula: Area = ½ × Base × Height. The height must be the perpendicular (90°) distance from the base to the opposite vertex, not the slant length of the side. For a right triangle, the two legs are the base and height. For an acute or obtuse triangle, you may need to extend the base line and drop a perpendicular from the apex to measure the true height.
For a triangular patio corner: if the two sides meeting at the right angle are 8 ft and 6 ft, the area is ½ × 8 × 6 = 24 sq ft. Order enough pavers for 24 sq ft plus 15% waste for the diagonal cuts at the hypotenuse edge.
Heron's Formula — Three Sides Method
When you cannot access the perpendicular height, measure all three sides and use Heron's formula:
- Step 1: Calculate the semi-perimeter: s = (a + b + c) ÷ 2
- Step 2: Calculate area: Area = √[s × (s−a) × (s−b) × (s−c)]
Example: A triangular garden bed with sides 10 ft, 8 ft, and 7 ft. s = (10+8+7)/2 = 12.5. Area = √[12.5 × 2.5 × 4.5 × 5.5] = √[773.4] = 27.8 sq ft. Our calculator performs this automatically — just enter the three side lengths.
Triangle Applications in Construction
- Gable end wall: ½ × ridge width × gable height. For a 24 ft wide house with a 6 ft gable: ½ × 24 × 6 = 72 sq ft of siding needed on each end.
- Triangular corner garden bed: Measure two side lengths meeting at the right angle; area = ½ × side A × side B.
- Hip roof section: each triangular hip section = ½ × eave width × slant height of hip rafter.
- Triangular patio: ½ × base × height; add 15% waste for diagonal tile cuts.
- Sail shade: triangle area determines the fabric panel size ordered from the manufacturer.
Converting Triangle Area to Material Quantities
Add 15% waste for triangular areas when ordering tile, pavers, or composite decking — the diagonal cuts at the hypotenuse produce more unusable offcuts than rectangular cuts. For grass seed, mulch, or gravel on a triangular bed, the waste factor is essentially zero because bulk materials have no cut waste. Seed at the same rate per square foot regardless of shape.
Related tools: trapezoid calculator · polygon calculator · irregular shape · roof calculator
Triangle Area in Landscaping and Site Work
Triangular areas are common in site grading, drainage swales, and corner lot landscaping. A triangular drainage swale with a base of 15 ft and a perpendicular depth of 6 ft has an area of 45 sq ft. At 4 inches of topsoil depth, the volume is 45 × 0.333 = 15 cubic feet = 0.56 cubic yards. Corner garden beds cut at 45 degrees from a house corner create right triangles — the two legs equal the setback distance from the house on each side. A 6 ft × 6 ft corner bed: ½ × 6 × 6 = 18 sq ft. At 3 inches of mulch depth: 18 × 0.25 / 27 = 0.17 cubic yards of mulch — approximately 2.25 bags of 2 cu ft mulch.