Answer:
Area = 45.0 square units
Perimeter= 34.1 unit long
Step-by-step explanation:
O(-4,-3), P(-6,5), and D(7,-2)
We fist find the length of the sides using Coordinate Geometry.
Distance between two points
= √[(x₂-x₁)²+(y₂-y₁)²]
When O(-4,-3), P(-6,5)
OP = √[(-6-(-4))²+(5-(-3))²]
= √[(-6+4)²+(5+3)²]
=√[(-2)²+(8)²]
=√[4+64]=√68 =2√17
O(-4,-3), D(7,-2)
OD = √[(7-(-4))²+(-2-(-3))²]
= √[(7+4)²+(-2+3)²]
=√[(11)²+(1)²]
=√[121+1]=√122
P(-6,5), D(7,-2)
PD = √[(7-(-6))²+(-2-5)²]
= √[(7+6)²+(-7)²]
=√[(13)²+(7)²]
=√[169+49]=√218
(a)Perimeter=2√17+√122+√218 =34.1 unit
(b) Height=6.1 units long
Area of a triangle = ½ base X Height
=½ X PD X Height
=½ X √218 X 6.1 = 45.0 square units
