Question

Find the area of the triangle formed by the points (2,3),(6,3) and(2,6)using heron's formula ​

Answer 1

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Answer 2

Solution:-

Let Point A = ( 2,3)

Point B = ( 6,3)

Point C = ( 2,6).

Using Distance Formula,

=) AB = √[ (6-2)² + (3-3)²]

=) AB = √ [ 4² + 0]

=) AB = 4.

Now, Using Distance Formula,

=)BC = √[ (2-6)² + (6-3)²]

=) BC = √[ ( -4)² + (3)²]

=) BC = √[ 16 + 9]

=) BC = √25

=) BC = 5.

Again Using Distance Formula,

=) AC = √[ (2-2)² + (6-3)²]

=) AC = √[ 0 + 3²]

=) AC = 3.

Now,

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

=) s = ( 5 + 4 + 3)/2

=) s = 12/2

=) s = 6.

Area of Triangle = √[ s (s-a)(s-b)(s-c)]

=) Area = √[ 6 (6-4)(6-5)(6-3)]

=) Area = √[ 6 × 2 × 1 × 3]

=) Area = √ [ 2 × 3 × 3 × 2]

=) Area = 2×3

=) Area = 6 sq. units.