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

Let us give a name for each vertex:
A(-5,7), B(5,4), and C(7,-8)

a) First Step: Find the lengths of side AB, AC, and BD
Using the distance formula: d = √[(x2 - x1)^2 + (y2 - y1)^2].

dAB = √[(xb - xa)^2 + (yb - ya)^2]
dAB = √[(5 - -5)^2 + (4 - 7)^2]
dAB = 10.44

dAC = √[xc - xa)^2 + (yc - ya)^2]
dAC = √[(7 - - 5)^2 + (-8 - 7)^2]
dAC = 19.21

dBC = √[(xc - xb)^2 + (yc - yb)^2]
dBC = √[(7 - 5)^2 + (-8 - 4)^2]
dBC = 12.17

Using Hero's Formula for obtaining the area of a triangle whose sides are known:
S = √[s(s - dAB)(s - dAC)(s - dBC)]
where S = area of the triangle
s = (1/2)(dAB + dAC + dBC)

Solving for s:
s = (1/2)(10.44 + 19.21 + 12.17)
s = 20.91

Area of triangle ABC = S = √[s(s - dAB)(s - dAC)(s - dBC)]
S = √[20.91(20.91 - 10.44)(20.91 - 19.21)(20.91 - 12.17)]
S = 57.03 square units ANS


teddy boy

Answer 2

If you do graph this problem, another way to solve it besides 1/2 base times height is to box the triangle in. After doing this you can find the areas of the surrounding shapes and the area of the rectangle, subtract the areas of the other shapes from the rectangle's area, and then you have the area of the triangle.

Answer 3

Hello...
it's a little bit complicated to write mathematical terms here :( but i try

Have you ever heard from the vectorial product?? i think it is the simplest way for this problem.
let consider these points
a(-5,7), b(5,4), c(7, -8) and the vectors A(from a to b), B (from b to c) and C (from c to a)

A = (10, -3), B = (2, -12) and C = (-12, 15)

the area of the triangle is
module (of the vectorial product of the vectors (A) and (B) ) divided by two...

this module is after computing egal to 114 so the area is 57...

Note that you would get the same values it you use the module (of the vectorial product of the vectors (B) and (C) ) and even that of the vectors (C) and (A)

Answer 4

area of a triangle is 1/2 base times height
1/2bh
sry i dont kno if this is what u were looking for or not but i hoped i helped

Answer 5

to find the area of a triangle you multiply base times height divided by two .................... so if the base was two and the height was six the answer would be 6 b/c 6 times 2 is 12 and 12 divided by two is 6