Triangle area calculator

Area is a numerical characteristic of a two-dimensional (flat or curved) geometric figure, informally speaking, showing the size of this figure. Historically, the calculation of the area was called quadrature. A figure having an area is called quadratic. Find the area of more than 22 shapes (triangle, square, pentagon, etc.) using our amazing calculator.

Triangle — is a geometric figure that has three points that do not lie on the same line and three segments that pair these points in pairs. The points of a triangle are usually called its vertices, and the segments are called its sides.

Triangles are a fascinating geometric shape, and understanding their area is important in many fields, such as engineering and construction. While finding the area of a triangle can be challenging, our online triangle area calculator makes it quick and simple.

• Triangle area through base and height
• Triangle area through three sides
• Through two sides and the angle between them
• Across the side and adjacent corners
• Through the radius of the inscribed circle
• Through the radius of the circumscribed circle
• Right triangle area
• Isosceles triangle area
• Equilateral triangle area

Triangle area through base and height

Let's start with a basic definition: A triangle is a polygon with three sides. To calculate the area of a triangle, there are three main formulas that are commonly used. The first one is the `base and height` formula, which is used when the base and height of the triangle are known. The formula for this:

S = \dfrac{ah}{2}

where S is the triangle area, a is the base and h is the height of the triangle.

Triangle area through three sides

The second formula is Heron's Formula, which is used when all three sides of the triangle are known. This formula is a bit more complex, as it involves the semi-perimeter of the triangle and the lengths of each of its sides. The formula is:

S = \sqrt{p(p-a)(p-b)(p-c)}

where S is the triangle area, a, b and c are the lengths of the sides and p is the semi-perimeter of the triangle.

Through two sides and the angle between them

The third formula is the `area of a triangle with sides and angle between them` also known as `area of triangle by sides and angle`. This formula is used when the sides of the triangle and the angle between them are known. The formula for this is S = \dfrac{a*b*sin(C)}{2}
where a and b are the sides of the triangle and C is the angle between them.

Across the side and adjacent corners

In addition to the three main formulas that are discussed above, there is also another method to calculate the area of a triangle which is through the measurement of one side and the adjacent corners. This formula is known as the `across the side and adjacent corners` and is especially useful when working with right triangles. The formula is: S = \dfrac{a^2*sin(α)*sin(β)}{2sin(γ)}
This formula can be applied when the length of one side of the triangle and the angles of the two adjacent corners are known.

Through the radius of the inscribed circle

Another method to find the area of a triangle is through the radius of the inscribed circle. The inscribed circle, also known as the incircle, is a circle that is completely inside the triangle and touches each of its sides. The radius of the inscribed circle is known as the inradius, and its value can be used to calculate the area of the triangle. The formula is:

S = pr

Where S is triangle area, r is the radius of the inscribed circle and p the semi-perimeter of the triangle.

Through the radius of the circumscribed circle

Another method to find the area of a triangle is through the radius of the circumscribed circle. The circumscribed circle, also known as the circumcircle, is a circle that passes through all three vertices of the triangle and is tangent to each of its sides. The radius of the circumcircle is known as the circumradius, and its value can be used to calculate the area of the triangle. The formula is:

S = \dfrac{abc}{4R}

where a, b, and c are the lengths of the sides of the triangle and R is the circumradius.

Right triangle area

In addition to the previously mentioned methods, the area of a right triangle can also be found using a specific formula. A right triangle is a triangle that contains a 90-degree angle. The formula for finding the area of a right triangle is:

S = \dfrac{ac}{2}

which is the same formula used for finding the area of any triangle given its base and height. In a right triangle, the base and height are the lengths of two of its sides, and the third side is the hypotenuse, which is the longest side.

Isosceles triangle area

An isosceles triangle is a triangle that has two sides with the same length, and the third side has a different length. The height of an isosceles triangle can be found by drawing a perpendicular line from the midpoint of the equal sides to the base. The height divides such a triangle in half, an isosceles triangle divided into two right triangles and using the formula to find the area of a right triangle, we get the following formula:

S = \dfrac{b\sqrt{a^2-\dfrac{b^2}{4}}}{2}

Equilateral triangle area

An equilateral triangle is a special type of isosceles triangle where all three sides are of equal length. If the length of the sides of an equilateral triangle is known, the formula can be used to find its area.

S = \dfrac{\sqrt{3}}{4}a^2

With our online triangle area calculator, you can easily find the area of a triangle by selecting the formula you want to use and inputting the required measurements.
Whether you know the base and height, all three sides, or the sides and an angle, our calculator will provide you with accurate results in no time.

To use our calculator simply select the formula that corresponds to the information you have, input your measurements, and let our calculator do the rest. No more struggling with complicated formulas or wasting time trying to figure it out on your own. Try our calculator today and see just how easy it can be!