A triangle is a figure closed by three line segments. The line segments are known as sides Of the triangle. The area covered by the triangle is known as the triangle area. The Triangle area can be calculated in many ways. Here triangle area calculator is based on the height of the triangle and base length of the triangle.
Fill the Triangle Base and Height and Hit Calculate Button
Triangle Area Calculator | |
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Height | 0 |
Base | 0 |
Area ( Height x base /2 ) | 0 |
In the previous part, we learned that area of the triangular region = 1/2 * base * height. In the following part, we have added some other relevant formulas
Let in the right-angled triangle ABC, BC = a, and AB = b are the adjacent sides of the right angle. Here if we consider BC as the base and AB as the height
Area of ABC = 1/2 × base × height = 1/2 ab
Two sides of a triangular region and the angle included between them are given
Let in ABC, the sides are
BC = a, CA = b, AB =c.
AD is drawn perpendicular from A to BC. Let altitude (height) AD = h.
Considering the angle C we get, AD / CA = sinC
or, h/b = sinC or, h = bsinC
Area of ABC = 1/2 × BC × AD
Area of ABC = 1/2 × BC × AD
= 1/2 a × b sinC = 1/2 × absinC
Similarly, area of ABC = 1/2 bcsinA =1/2 casinB
Three sides of a triangle are given
Let in ABC, BC = a, CA = b and AB = c.
Perimeter of the triangle 2s = a + b + c.
We draw AD ⊥ BC.
Let, BD = x, then CD = a − x
In right-angled ABD and ACD
AD² = AB² − BD² and AD² = AC² − CD²
AB² − BD² =AC² − CD²
or, c² − x² = b² − (a − x)²
or, c² − x² = b² − a² + 2ax − x²
or, 2ax = c² + a² − b²
x = c² + a² − b²/ 2a
Again,
AD² = c² − x²
AD² = c² − (c² + a² − b²/ 2a)²
AD² = (c + c² + a² − b²/ 2a) (c - c² + a² − b²/ 2a)
AD² = (2ac + c² + a² − b²/ 2a) (2ac - c² + a² − b²/ 2a)
AD² = {(c + a)² − b² } {b² − (c − a)² }/4a²
AD² = (a + b + c) (a + b + c − 2b) (a+ b + c − 2a) (a+ b + c − 2c)/ 4a²
AD² = 2s(2s − 2b)(2s − 2a)(2s − 2c)/4a²
AD² =4s(s − a)(s − b)(s − c)/a²
AD = 2/a √s(s − a)(s − b)(s − c)
Area of ABC = 1/2 BC × AD
=1/2 x a x 2/a √{s(s − a)(s − b)(s − c)}
=√{s(s − a)(s − b)(s − c)}
Equilateral triangle: Let the length of each side of the equilateral triangular region ABC be a.
Draw AD ⊥ BC.
BD = CD = a/2
In right-angled ABD
BD² + AD² = AB²
or, AD² = AB² − BD² = a² − (a/2)²
or, AD² = a² − a²/4
or, AD² =4a² − a²/4
AD = √3a/2
Area of ABC = 1/2 BC × AD
= 1/2 × a × √3a/2=√3/4 a²
Let ABC be an isosceles triangle in which
AB = AC = a and BC = b
Draw, AD is perpendicular BC. BD = CD = b/2
ABD is right angled.
AD² = AB² − BD²
AD² = a² − (b/2)²
AD² = a² − b²/4
AD² = (4a² − b²)/4
AD = √(4a² − b²)/2
Area of isosceles ABC = 1/2 BC × AD
= 1/2 × b × √(4a² − b²)/2
= b/4 √(4a² − b²)