How would I find the area of...?

Question

A triangle with the following vertices: (-5, 7), (5, 4), (7, -8). I know this is extremely easy, but I simply forgot the procedure. Help?

Answer 1

You just plot those points and find the distance between each pair of points that makes the base and height. That is, use the distance formula to find the distance between the two points that connect to form the base and the two that connect to form the height once you draw it out. Now you will have numbers for which you can plug into A=(1/2)Bh
You take it from here!

Answer 2

One way is to use the distance formula to find the length of eac side. Then you can use Hero's formula to compute the area.

Another way is to compute the length of just one side and then also compute that side's slope. Take the negative reciprocal of that .slope and find the altitude to taht side from the opposite vertex. Find the length of the altitude and then us A = base X altitude /2/

Answer 3

Let us give names to the vertices:
A(-5,7), B(5,4), C(7,-8)

Solving for the lengths of the three side:
AB = √[(xb - xa)^2 + (yb - ya)^2]
AB = √[(5 - -5)^2 + (4 - 7)^2]
AB = 10.4

AC = √[(xc- xa)^2 + (yc - ya)^2]
AC = √[(7 - -5)^2 + (-8 - 7)^2]
AC = 19.2

BC = √[(xc - xb)^2 + (yc - yb)^2]
BC = √[(7 - 5)^2 + (-8 - 4)^2]
BC = 12.2

By Hero's Formula:
S = √[s(s - AB)(s - AC)(s - BC)]
Where S is the area of the triangle whose three sides are known
s = (1/2)(AB + AC + BC)
s = (1/2)(10.4 + 19.2 + 12.2)
s = 20.9

S = √[s(s - AB)(s - AC)(s - BC)]
S = √[20.9(20.9 - 10.4)(20.9 - 19.2)(20.9 - 12.2)]
S = 56.97 ANS

teddy boy