18 unitsΒ²
step-by-step explanation:
first let's find altitude bd using the distance formula
d = β((yβ - yβ)Β² + (xβ - xβ)Β²)
bd = β((0 - -3)Β² + (0 - 3)Β²)
bd = β18
given the placement of points a and c, we can denote that point d bisects segment ac.
we will call ac the base.
using the distance formula
ac = β((0 - 6)Β² + (-6 - 0)Β²)
ac = β72
knowing our base and our height, we can plug these into our triangle area formula
area = (b * h)/2
area = (β18 * β72) / 2
area = (β1296) / 2
area = 36 / 2
area = 18 unitsΒ²