Triangle OPD has coordinates O(-4,-3), P(-6,5), and D(7,-2). The height of OPD that runs from vertex O to PD is 6.1 units longs. Determine the perimeter and area of OPD. Round your answer to th enearest unit.

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

a

step-by-step explanation: