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? !

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
 
 The area, in square units, of triangle QRS is:
 A = 7 units ^ 2

Hey there! :)

The formula for finding volume of a cone = (π · r² · h) ÷ 3

r = 3
3² = 3 × 3 = 9

h = 7

7 × 3 × π = 21π

Your answer is C. 21π³

Hope this helps :)