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In geometry, we may have come across a variety of different types of formulas, such as perimeter, area, height, volume, and other similar terms. When working with polygons, one of the most frequently encountered metrics is the semi perimeter. It is a measurement that is associated with plane figures, which are two-dimensional shapes. Simple formulas can be used to compute the semi perimeter of a variety of various plane figures. In this post, you will discover the definition of semi perimeter, as well as the formula for semi perimeter for various forms, as well as instances of the two terms used.
As we all know, the perimeter of a shape is the distance around it, but the semi perimeter is half the distance around it. The semi perimeter of a given polygon can be computed by dividing its circumference by two for each given polygon. Despite the fact that it is derived from the perimeter in a straightforward manner, the semi perimeter appears frequently in formulas relating to triangles and other shapes, prompting it to be given a separate name. A semi perimeter is represented by the letter “s” in a formula when it is a part of the formula.
Semi Perimeter Formula
The formula is Semi perimeter = Perimeter/2.
However, the following table has semi perimeter calculations for a variety of shapes and polygons:
Shape | Formula | Explanation |
Semi Perimeter of a Triangle formulas | ||
Equilateral triangle | 3a/2 | a = Length of the side of an equilateral triangle |
Isosceles triangle | a + (b/2) | a = Length of congruent sides b = Length of the third side |
Right angle triangle | (base + height + hypotenuse)/2 | Height = Perpendicular Hypotenuse = The longest side |
Scalene triangle | (a + b + c)/2 | a, b, c are the measures of lengths of three sides |
Semi Perimeter of Curved Shapes Formulas | ||
Circle | (2πr)/2 or πr | r = Radius of circle |
Semicircle | (πr + 2r)/2 | r = Radius of the semicircle |
Semi Perimeter of Quadrilaterals Formulas | ||
Rectangle Formula | 2(l + b)/2 or l + b | l = Length b = Breadth |
Square | (4a/2) or 2a | a = Side of a square |
any quadrilateral | (a + b + c + d)/2 | a, b, c, d are the length of sides of the quadrilateral |
Semi Perimeter of triangle
It is possible to calculate the semi perimeter of a triangle by dividing the total perimeter of the triangle by two. Due to the fact that semi’ signifies half, the semi perimeter of a triangle is equal to half the value of the perimeter. In order to determine the area of a triangle using Heron’s formula, the semi perimeter of a triangle must be known. It is possible to express the semi perimeter of a triangle in linear units such as inches, yards, millimetres, and so on. After that, we will go over the formula that is used to calculate the semi-perimeter of a triangular shaped figure. Knowing that the perimeter of a triangle is equal to the sum of the lengths of all its sides, we can calculate its area. Take, for example, a triangle with three equal-length side lengths (a, b and c). The perimeter of the triangle may be computed using this formula: Perimeter = (a+b+c). As a result of using this technique, The semi-perimeter of a triangle is equal to (a + b + c)/2.
Use of the Semi perimeter of Triangle in heron’s formula
When the lengths of all three sides of a triangle are known, the semi perimeter of a triangle can be used to calculate the area of a triangle using Heron’s formula. It is only the lengths of all the triangle’s sides that determine the outcome of this calculation. A semi perimeter is represented by the letter “s,” which is obtained by dividing the perimeter of a triangle by two and is represented by the letter “s.” This is the Heron’s formula, which is written as√[s(s-a)(s-b)(s-c)], where s denotes the Semi-Perimeter of the triangle and the letters a’, ‘b’, ‘c’ denote the three sides of the triangle. This yields the area of a triangle whose three sides are known in advance of time.
Perimeter of a Semicircle Formula
When calculating the perimeter of a semicircle, the formula for the perimeter of a semicircle is utilised. We must know the diameter or radius of a circle, as well as the length of an arc, in order to solve this problem. In order to get the length of the arc of the semicircle, we must first determine the circumference of a circular figure.
The circumference of a circle is given by the formula C = πd or C = 2πr.
When we take into account the value of C, we can come up with a formula to compute the perimeter of a semicircle, which is determined as the sum of half of a circle’s circumference and the diameter of a circle.
The perimeter of a semicircle is calculated using the formula(πR + d) or (πR + 2R), or R(π + 2)units.
where R = radius of a semicircle
π(pi) is 22/7 or 3.142 and,
d = Diameter of a semicircle.
Conclusion
It is possible to calculate the semi perimeter of a triangle by dividing the total perimeter of the triangle by two. Due to the fact that semi’ signifies half, the semi perimeter of a triangle is equal to half the value of the perimeter. In order to determine the area of a triangle using Heron’s formula, the semi perimeter of a triangle must be known.
