Question

If A ( 0,5) ,B(6,11)and C (4,5) are the vertices of a ABC

Answer 1

Before we find the area of the triangle, let us know its formula:

Let (x1, y1), (x2, y2) and (x3, y3) are the coordinates of the vertices of a triangle.

The area of the triangle is given by

| x1 y1 1 |

= 1/2 * | x2 y2 1 | square units

| x3 y3 1 |

= 1/2 * {x1 (y2 - y3) + x2 (y3 - y1) + x3 (y1 - y2)} square units [ expanding along the first column ]

Note: we take the modulus value only.

Now we proceed to solve the problem:

The vertices of the given triangle are A (0, 5), B (6, 11) and C (4, 5).

Using the above formula, we find the area of ABC triangle

= 1/2 * {0 (11 - 5) + 6 (5 - 5) + 4 (5 - 11)} square units

= 1/2 * (0 + 0 - 24) square units

= 12 square units (modulus value)

Therefore the area of the triangle is 12 square units.

Related problems:

1. Prove that the area of triangle whose vertices are (5, 2), (- 9, - 3) & (- 3, - 5) is four times the area of the triangle formed by joining the mid points of the sides. - https://brainly.in/question/12414613
2. If A (0, 5), B (6, 11 ) and C (10, 7) are the vertices of a triangle ABC, D and E are the mid-points of AB and AC respectively. Then find the area of the triangle ADE. - https://brainly.in/question/15433738