Question

The venticles of a right angle are a[0,4], b[3,-2] c[-3, -4] Find It's area.​

Answer 1

The area of this triangle is about 21.2132 square units.

Explanation:

First, find the lengths of the legs AB and BC.

Length of AB ===

Find the difference in position vertically:

`-2-4=-6`

The points are 6 units apart vertically.

Find the difference in position horizontally:

`3-0=3`

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:

`a^2+b^2=c^2\\3^2+6^2=c^2\\9+36=c^2\\45=c^2\\c\approx6.7082`

AB is about 6.7082 units long.

Length of BC ===

Same process as above.

Find the vertical distance:

`-4--2=-2`

2 units apart vertically.

Find the horizontal distance:

`-3-3=-6`

6 units apart horizontally.

Use the pythagorean theorem:

`2^2+6^2=c^2\\4+36=c^2\\40=c^2\\c=6.3246`

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:

`A=(b* h)/(2)\\\\A=(6.7082*6.3246)/(2)\\\\A=(42.4264)/(2)\\\\A=21.2132`

The area of this triangle is about 21.2132 square units.