Geometry

[Ashiya]

Hi,

I need to find the area of triangle where the vertices are given
A= (?3, 5)

B= ( -?3 ,0)

C= (?5, 0)


Thanks,

Ashiya

 

[Loren]

Did you draw a sketch on a rectangular coordinate system graph? If you did, it would have become quite apparent as to the altitude of the triangle. Also, the base of the triangle is easily obtained by addition. Then, of course, you know the formula for the area of a triangle. It may look funny because it will have a couple of radical signs in the answer, unless you are permitted to use a calculator, in which case there will be a decimal point. Don't forget that the area will be expressed in square units. Go for it.

 

[mmm4444bot]

For more fun, you could use the following formula to verify your result.

Given the coordinates of three vertices: (a, b) (c, d) (e, f)

The area of the triangle is:

\(\displaystyle \left| \frac{(a - c) \cdot (d - f) - (c - e) \cdot (b - d)}{2} \right|\)

Use a calculator to compare the decimal approximation of your result with the result from using the formula above.

 

[pka]

I need to find the area of triangle where the vertices are given
A= (?3, 5) , B= ( -?3 ,0) , C= (?5, 0)

It is clear that the altitude has length \(\displaystyle 5\).
The base has length \(\displaystyle \sqrt{5} + \sqrt{3}\).
What is the area?