Answer:
16 units
Step-by-step explanation:
The area of a rhombus is given by the formula A = bh. The base would be CB and the height would be DP. We will use the distance formula to find the length of each:
[tex]d=\sqrt{y_2-y_1)^2+(x_2-x_1)^2}[/tex]
For CB, we have
[tex]d=\sqrt{(2-0)^2+(3--1)^2}=\sqrt{2^2+4^2}=\sqrt{4+16}=\sqrt{20}[/tex]
For DP we have
[tex]d=\sqrt{(2--1.2)^2+(-5--3.4)^2}=\sqrt{3.2^2+1.6^2}=\sqrt{10.24+2.56}=\sqrt{12.8}[/tex]
This makes the area of the rhombus
[tex]A=bh=\sqrt{20}\times \sqrt{12.8}=\sqrt{20\times 12.8}=\sqrt{256}=16[/tex]
