Answer:
The area of rhombus = 24
Step-by-step explanation:
The area of rhombus = base times height
For the given rhombus :
Height = The length of DP
Base = the length of any side of the rhombus as AB
The length ot two point (x₁ , y₁) and (x₂ , y₂) = [tex]\sqrt{(x_{1} -x_{2} )^2+(y_{1} -y_{2})^2}[/tex]
From the given figure:
D = (-5,-2) , P = (-3.8 , 1.6) , A = (1,0) , B = (7 , -2)
DP = [tex]\sqrt{(-5-(-3.8))^2+(-2-1.6)^2}[/tex] = √14.4
AB = [tex]\sqrt{(1-7)^2+(0-(-2))^2}[/tex] = √40
So,
The area of rhombus = √14.4 * √40 = √576 = 24
