Answer:
The area of this triangle is about 21.2132 square units.
Step-by-step explanation:
First, find the lengths of the legs AB and BC.
Length of AB ===
Find the difference in position vertically:
[tex]-2-4=-6[/tex]
The points are 6 units apart vertically.
Find the difference in position horizontally:
[tex]3-0=3[/tex]
The points are 3 units apart horizontally.
These lengths form a right triangle with the distance between the points as the hypotenuse, so you can use the pythagorean theorem to solve:
[tex]a^2+b^2=c^2\\3^2+6^2=c^2\\9+36=c^2\\45=c^2\\c\approx6.7082[/tex]
AB is about 6.7082 units long.
Length of BC ===
Same process as above.
Find the vertical distance:
[tex]-4--2=-2[/tex]
2 units apart vertically.
Find the horizontal distance:
[tex]-3-3=-6[/tex]
6 units apart horizontally.
Use the pythagorean theorem:
[tex]2^2+6^2=c^2\\4+36=c^2\\40=c^2\\c=6.3246[/tex]
BC is about 6.3246 units long.
Area ===
Finally, you can use these to find the area of the triangle. The area of a right triangle is just half the area of a rectangle with the same base and height:
[tex]A=\frac{b\times h}{2}\\\\A=\frac{6.7082\times6.3246}{2}\\\\A=\frac{42.4264}{2}\\\\A=21.2132[/tex]
The area of this triangle is about 21.2132 square units.
