Given triangle abc with vertices A(2,-1), B(5,6), C(-1,4) as shown. Find the number of square units in the area of triangle abs in simplest form.

The area of the triangle is 18 square units.

Step-by-step explanation:

First, we determine the lengths of segments AB, BC and AC by Pythagorean Theorem:

AB

BC

AC

Now we determine the area of the triangle by Heron's formula:

(1)

(2)

Where:

- Area of the triangle.

- Semiparameter.

If we know that , and , then the area of the triangle is:

The area of the triangle is 18 square units.

5050

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