# Calculate the area of the triangle with the following points:(-4, -10), (1, -3), (-2, -5)

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### 2 Answers

Given the vertices's of the triangle are: (-4, -10) (1,-3) and (-2,-5)

We will find the lnegth of the sides using the distance between two points formula.

==> D1 = sqrt( -4-1)62 + (-10+3)^2 = sqrt( 25 + 49) = sqrt(74)= 8.6

==> D2 = sqrt( -4+2)^2 + (-10+5)^2 = sqrt( 4 + 25) = sqrt(29)= 5.39

==> D3 = sqrt( 1+2)^2 + (-3+5)^2 = sqrt( 9 + 4) = sqrt13=3.61

Now we will find the perimeter.

==> P = 8.6 + 5.39 + 3.61 = 17.6

==> s = p/2 = 17.6/2 = 8.8

Now we will find the area.

==> A = sqrt s( s-a)(s-b) (s-c)

==> A = sqrt( 8.8 * 5.19 * 3.41 * 0.2)

==> A = sqrt( 31.15) = 5.6

**Then the area of the triangle is 5.6 square units ( approx.)**

There is a formula that makes use of determinants.

S = (1/2)*Determinant

|-4 -10 1|

Determinant = |1 -3 1|

|-2 -5 1|

We'll calculate the determinant:

D = (-4)*(-3)*1 + 1*(-5)*1 + (-2)*(-10)*1 - (-2)*(-3)*1 - 20 + 10

D = 11

**The area of the given triangle is: S = 11/2 = 5.5 square units.**