Question

If (4,2) (6,5) (1,4) are the vertices of a triangle what is the area of the triangle

Answer 1

x1=4
x2=6
x3=1
Y1=2
Y2=5
y3=4
$\bold{ \pink{area \: of \: triangle \: = \frac{1}{2} (x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2))}} \\ \bold{ \green{ = \frac{1}{2} (4(5 - 4) + 6(4 - 2) + 1(2 - 5)}} \\ \bold{\green = \frac{1}{2} (4(1) + 6(2) + 1( - 3) )}\\ = \frac{1}{2} (4 + 6 - 3) \\ = \frac{1}{2} \times 7 \\ = \frac{7}{2} \\ = 3.5sq \: unit$

Answer 2

The vertices are  (4,2)(6,5)(1,4)

where    x1=4,  y1=2, x2=6, y2=5, x3=1 & y3=4

area of triangle = 1/2( x1 (y2-y3) + x2(y3-y1) + x3(y1-y2) )

 =1/2(4(5-4) + 6(4-4) + 1(2-5) )

=1/2( 4(1) + 6(0) + 1(-3))

=1/2 (4+0-3)

=1/2(1)

=1/2 ans

∴ area of triangle is 1/2