Question

Find the area of

(-2, 6), (-5, 2), (1, 3)

(-5, 2), (1, 3), (-3, -2)

(-3, -2), (1, 3), (4, -3)

(1, 3), (4, -3), (5, 3)

Answer 1

• 10.5
• 13
• 19.5
• 12

Explanation:

For a set of points (x1, y1), (x2, y2), (x3, y3), the area can be found as ...

Area = (1/2)|x1(y2-y3) +x2(y3-y1) +x3(y1-y2)|

The four areas are ...

Area1 = (1/2)|-2(2-3) -5(3-6) +1(6-2)| = |2+15+4|/2 = 10.5

Area2 = (1/2)|-5(3+2) +1(-2-2) -3(2-3)| = |-25-4+3|/2 = 13

Area3 = (1/2)|-3(3+3) +1(-3+2) +4(-2-3)| = |-18-1-20|/2 = 19.5

Area4 = (1/2)|1(-3-3) +4(3-3) +5(3+3)| = |-6+0+30|/2 = 12

_____

Confirmed by a geometry program (see attached).