Question

What is the area of a parallelogram ABCD

Answer 1

Answer:

Area of a parallelogram would be 13.46

Step-by-step explanation:

Since area of a parallelogram is represented by the formula

Area = $\frac{1}{2}$ ($(D_{1}*D_{2})$

Where $D_{1}$ and $D_{2}$ are two diagonals of the given parallelograms.

In the given figure $D_{1}=AC$ and $D_{2}$ = BD

We will find the length of $D_{1}$ and $D_{2}$ first

Since points A and C are (3,6) and (5,1)

So distance AC = $\sqrt{(6-1)^{2}+(3-5)^{2} }$

= $\sqrt{5^{2}+(-2)^{2}}$

= $\sqrt{25+4}=\sqrt{29}$

Since B and D are the points (6, 5) and (2, 2)

So length of BD = $\sqrt{(6-2)^{2}+(5-2)^{2}}$

BD = $\sqrt{4^{2}+3^{2}}=\sqrt{25}=5$

Now we will put these values in the formula

Area of parallelogram = $\frac{1}{2}(\sqrt{29})(5)$

= $\frac{5}{2}$ × $\sqrt{29}$

= (2.5) (5.385)

= 13.46