30
sq units
—
acres
0.003
hectares
30
sq units
—
acres
0.003
hectares
The Triangle Area Calculator computes the area of any triangle using the simplest and most intuitive method: base times height divided by two. This fundamental formula, $$A = \frac{1}{2} \times b \times h$$, works for every triangle — acute, right, or obtuse — as long as you know the base length and the corresponding perpendicular height. Enter the base and height, and the calculator instantly returns the area along with convenient unit conversions.
The formula $$A = \frac{1}{2}bh$$ is one of the oldest and most widely used formulas in all of mathematics. It appears in virtually every ancient mathematical tradition: Egyptian papyri, Babylonian tablets, Chinese manuscripts, and Indian texts all contain versions of this calculation. The formula's simplicity belies its power — it reduces the measurement of any triangular region to two linear measurements.
Understanding why this formula works requires a key geometric insight. Any triangle can be enclosed in a rectangle (or parallelogram) with the same base and height. The triangle occupies exactly half of that rectangle. For a right triangle, this is visually obvious: the two legs form the base and height, and the triangle is literally half of the corresponding rectangle. For acute and obtuse triangles, the proof requires a bit more construction, but the result is the same: the triangle's area is always half the product of its base and the corresponding height.
The base can be any side of the triangle — you choose which side to call the base. The height (or altitude) is then the perpendicular distance from the base to the opposite vertex. For acute triangles, the height falls inside the triangle. For right triangles, one leg serves as the height. For obtuse triangles, the height from certain bases falls outside the triangle, but the formula still works because the height is defined as a perpendicular distance, not a side length.
This calculator is particularly useful in land surveying and real estate, where triangular plots of land must be measured. Surveyors often decompose irregular parcels into triangles, compute each triangle's area using base-height measurements, and sum the results. The calculator provides area conversions to acres (for measurements in feet) and hectares (for measurements in meters) to facilitate land area calculations.
In construction, triangular areas arise in gable walls, roof sections, decorative elements, and material cutting. Knowing the area helps estimate paint coverage, material quantities, and structural loads. In education, the base-height formula is typically the first area formula students learn, serving as a gateway to more advanced area methods like Heron's formula, the cross product method, and integration.
For situations where you know three sides but not the height, consider using the general Triangle Calculator which employs Heron's formula. For right triangles, the two legs serve directly as base and height. This calculator is optimized for the common case where base and height are directly measured or given.
The area of a triangle with base $$b$$ and corresponding perpendicular height $$h$$ is:
$$A = \frac{1}{2} \times b \times h$$
Derivation: Consider a triangle with base $$b$$ on a horizontal line and apex at height $$h$$ above the base. Construct a rectangle with the same base $$b$$ and height $$h$$. The rectangle has area $$b \times h$$. The triangle can be shown to occupy exactly half this rectangle through dissection: the parts of the rectangle outside the triangle can be rearranged to fill the triangle exactly, proving that the triangle's area is $$\frac{bh}{2}$$.
Unit Conversions:
If the base and height are in feet:
$$A_{\text{acres}} = \frac{A_{\text{sq ft}}}{43{,}560}$$
If the base and height are in meters:
$$A_{\text{hectares}} = \frac{A_{\text{sq m}}}{10{,}000}$$
Key Properties:
The Area represents the total surface enclosed by the triangle, expressed in square units of whatever unit you used for the base and height. If you entered centimeters, the area is in square centimeters. If you entered meters, the area is in square meters.
The Area in Acres conversion assumes the base and height were entered in feet. One acre equals 43,560 square feet. This is useful for land area calculations in countries using the imperial system.
The Area in Hectares conversion assumes the base and height were entered in meters. One hectare equals 10,000 square meters. This is the standard land area unit in the metric system.
Remember that the height must be perpendicular to the base. If you measure the slant distance from the base to the opposite vertex (rather than the perpendicular distance), the calculated area will be incorrect. Always ensure the height measurement forms a 90° angle with the base.
Inputs
Results
Area = 0.5 * 10 * 6 = 30 square units. If units are feet: 30 sq ft = 30/43560 = 0.000689 acres. If units are meters: 30 sq m = 30/10000 = 0.003 hectares. This is a straightforward calculation.
Inputs
Results
Area = 0.5 * 200 * 150 = 15,000 sq ft = 0.3444 acres. This represents a moderately sized triangular land parcel, roughly one-third of an acre. A surveyor might measure the base along a road and the perpendicular distance to the farthest property corner.
No. You can choose any side as the base, but you must then use the perpendicular height corresponding to that base (the perpendicular distance from the chosen base to the opposite vertex). The area will be the same regardless of which side you designate as the base.
The height is the perpendicular distance from the base to the opposite vertex. For a physical triangle, you can drop a plumb line from the apex to the base line and measure the vertical distance. For a triangle on paper, draw a line from the opposite vertex perpendicular to the base (or its extension) and measure its length.
This happens with obtuse triangles when the base is one of the sides adjacent to the obtuse angle. The height drops to the extension of the base rather than the base itself. The formula A = 0.5 * b * h still works correctly — just use the perpendicular distance, which is always positive.
Heron's formula calculates area from three sides without needing the height. The base-height formula is simpler but requires knowing the height. Both give the same result. Use base-height when the height is known; use Heron's formula when you know all three sides but not the height.
Yes. Any polygon can be decomposed into non-overlapping triangles (triangulation). Calculate each triangle's area and sum them. This is the standard method used in surveying, computer graphics, and geographic information systems (GIS) for computing areas of irregular shapes.
For a fixed base length and fixed perimeter, the triangle with maximum area is the isosceles triangle (the two non-base sides are equal). This is a consequence of the isoperimetric property. The height is maximized when the apex is directly above the midpoint of the base.
Roboculator Team
The Roboculator Team explains calculations, planning tools, and practical formulas in clear language for real-life situations.
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