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Setler [38]
2 years ago
15

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

Mathematics
1 answer:
givi [52]2 years ago
4 0

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:

-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=\frac{b\times h}{2}\\\\A=\frac{6.7082\times6.3246}{2}\\\\A=\frac{42.4264}{2}\\\\A=21.2132

The area of this triangle is about 21.2132 square units.

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