Find the area of the triangle with vertices: Q(4,4,-1), R(5,7,-2), S(3,2,-4).

The area of the triangle is 5.875 square units.

Step-by-step explanation:

First, we need to calculate the lengths of the triangle by means of Pythagorean Theorem:

Now, we can use the following formula to fid the area of the triangle (), measured in square units:

Where:

- Semiperimeter of the triangle, dimensionless.

, , - Sides of the triangle, dimensionless.

The semiperimeter can be determined by this:

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

The area of the triangle is 5.875 square units.

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584

answer:

it is general formula that is used to write value to its excet position

a11 a12 a13

a21 a22 a23

it is the example of order 2 by 3 matrix in this

a11 means value occur in 1 st row 1st column

a12 means value occurs in 1st row 2nd column

a13 means value occur in 1st row and 3rd column

a21 means value occurs in 2nd row and 1st column

a22 means value occurs in 2nd row and in 2nd column

a23 means value occurs in 2nd row and in 3rd column