Question

What is the area of rhombus ABCD ? Enter your answer in the box. Do not round at any steps.

Answer 1

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) = $\sqrt{(x_{1} -x_{2} )^2+(y_{1} -y_{2})^2}$

From the given figure:

D = (-5,-2) , P = (-3.8 , 1.6) , A = (1,0) , B = (7 , -2)

DP = $\sqrt{(-5-(-3.8))^2+(-2-1.6)^2}$ = √14.4

AB = $\sqrt{(1-7)^2+(0-(-2))^2}$ = √40

So,

The area of rhombus = √14.4 * √40 = √576 = 24