What is the area of triangle BZW if B(-4, -2), Z(8, 7), W(1, 8)?

Answer 1

calculate the side lengths of the triangle

BZ =15, BW = 5sqr5, ZW = 5sqr2

You could try using Heron's formula Area = sqr[(p)(p-15)(p-5sq5)(p-5sqr2)]

where p = half the perimeter= (15+5sqr5+5sqr2)/2 But that looks a little messy and tedious. There must be other ways. still, we could estimate it. The sides are almost 15-11-7 with semi-perimeter =16.5 then the area is about sqr(16.5)(1.5)(5.5)(9.5) = about 36

Another way is:

Find the equation of BZ and of the perpendicular line from the point W to the line BZ. They intersect at (4,4) BZ =15. (4,4) to W is 5

The Area = bh/2 = 15(5)/2 = 75/2 = 37.5

BZ is y=3x/4 +1

the perpendicular through W is y=-4x/3 + 28/3

3x/4 + 1 = -4x/3 + 28/3

4x/3 +3x/4 = 25/3

25x/12 = 25/3

x/12 = 1/3

x=12/3 =4

y=3(4)/4 +1 = 4

from (4,4) to W = 5

(1,8) to (4,4) is sqr(3^2 +4^2) = sqr25 = 5