Question

What is the area of rhombus ABCD ?

Answer 1

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:

$d=\sqrt{y_2-y_1)^2+(x_2-x_1)^2}$

For CB, we have

$d=\sqrt{(2-0)^2+(3--1)^2}=\sqrt{2^2+4^2}=\sqrt{4+16}=\sqrt{20}$

For DP we have

$d=\sqrt{(2--1.2)^2+(-5--3.4)^2}=\sqrt{3.2^2+1.6^2}=\sqrt{10.24+2.56}=\sqrt{12.8}$

This makes the area of the rhombus

$A=bh=\sqrt{20}\times \sqrt{12.8}=\sqrt{20\times 12.8}=\sqrt{256}=16$

Answer 2

The answer is 16units