Question

Use Heron’s formula in different triangles to understand the incentre of a

triangle.

and Make conjectures and describe relationship between the area of triangle

using Heron’s theorem and traditional formula.​

Answer 1

Answer:

According to Heron, we can find the area of any given triangle, whether it is a scalene, isosceles or equilateral, by using the formula, provided the sides of the triangle.

According to Heron, we can find the area of any given triangle, whether it is a scalene, isosceles or equilateral, by using the formula, provided the sides of the triangle.Suppose, a triangle ABC, whose sides are a, b and c, respectively. Thus, the area of a triangle can be given by;

According to Heron, we can find the area of any given triangle, whether it is a scalene, isosceles or equilateral, by using the formula, provided the sides of the triangle.Suppose, a triangle ABC, whose sides are a, b and c, respectively. Thus, the area of a triangle can be given by;Area=s(s−a)(s−b)(s−c)−−−−−−−−−−−−−−−−−√

According to Heron, we can find the area of any given triangle, whether it is a scalene, isosceles or equilateral, by using the formula, provided the sides of the triangle.Suppose, a triangle ABC, whose sides are a, b and c, respectively. Thus, the area of a triangle can be given by;Area=s(s−a)(s−b)(s−c)−−−−−−−−−−−−−−−−−√Where “s” is semi-perimeter = (a+b+c) / 2

According to Heron, we can find the area of any given triangle, whether it is a scalene, isosceles or equilateral, by using the formula, provided the sides of the triangle.Suppose, a triangle ABC, whose sides are a, b and c, respectively. Thus, the area of a triangle can be given by;Area=s(s−a)(s−b)(s−c)−−−−−−−−−−−−−−−−−√Where “s” is semi-perimeter = (a+b+c) / 2And a, b, c are the three sides of the triangle.

Answer 2

Answer:

Example 1: If the length of the sides of a triangle ABC are 4 in, 3 in, and 5 in. Calculate its area.

Solution: To find: Area of the triangle ABC.

Given that, AB = 4 in, BC = 3 in, AC = 5 in (let)

Using Heron's Formula,

A = √(s(s-a)(s-b)(s-c))

As, s = (a+b+c)/2

s = (4+3+5)/2

s = 6 units

Put the values,

A = √(6(6-4)(6-3)(6-5))

⇒ A = √(6(2)(3)(1))

⇒ A = √(36) = 6 in2

∴ The area of the triangle is 6 in2.