Question

Triangle QRS, with vertices Q(6, -2), R(4, -7), S(2, -5), is drawn inside a rectangle, . What is the area, in square units, of triangle QRS?

HELP!

Answer 1

We look for the distance between each one of the vertices applying the following formula:
d = root ((x2-x1) ^ 2 + (y2-y1) ^ 2)
For QR:
QR = root ((4-6) ^ 2 + (-7 + 2) ^ 2)
QR = 5.385164807
For QS:
QS = root ((2-6) ^ 2 + (-5 + 2) ^ 2)
QS = 5
For RS:
RS = root ((2-4) ^ 2 + (-5 + 7) ^ 2)
RS = 2.828427125
Now we apply the heron formula:
A = root (s * (s-a) * (s-b) * (s-c))
Where,
s = (a + b + c) / 2
s = (5.385164807 + 5 + 2.828427125) / 2
s = 6.606795966
Substituting:
A = root (6.606795966 * (6.606795966-5.385164807) * (6.606795966-5) * (6.606795966-2.828427125))
A = 7.00000000
A = 7 units ^ 2
Answer:
The area, in square units, of triangle QRS is:
A = 7 units ^ 2