Question

find its area.......

Answer 1

This quadrilateral is a rhombus.

And the area==>>>

Let's divide the rhombus into two equal parts..

Now you seen that in the rhombus two triangles are formed.

Triangle ABD and Triangle BCD

So,if we find the area of this two triangles and after that add the areas of both the triangles then we will get the area of this quadrilateral.

So let's first find the area of triangle ABD

$\frac{1}{2} | - 4 \: \: - 6 \: \: - 2 \: \: - 4 | \\ \: \: \: | \: \: \: \: \: \: 4 \: \: \: \: \: \: \: \: 0 \: \: \: \: \: \: \: 0 \: \: \: \: \: \: \: \: 4 |$
$= \frac{1}{2} |( 0 + 0 - 8) - ( - 24 + 0 + 0)|$
$= \frac{1}{2} | - 8 + 24|$
$= \frac{1}{2} \times 16 \\ \\ = \frac{16}{2} \\ \\ = 8 \: sq..unite$

Now the area of triangle BCD

$\frac{1}{2} | - 6 - 4 - 2 - 6 | \\ \: \: \: | \: \: \: \: \: \: 0 - 4 \: \: \: \: \: 0 \: \: \: \: \: \: 0 |$
$= \frac{1}{2} |(24 + 0 + 0) - (0 + 8 + 0)|$
$= \frac{1}{2} |24 - 8|$
$=\frac{1}{2} \times 16 \\ \\ = \frac{16}{2} \\ \\ = 8 \: sq..unite$

Now we got the areas of both the triangles...

Now we easily find the area of this quadrilateral..

Area of quadrilateral ABCD = Area of triangle ABD + area of triangle BCD

By putting the obtained values we get.

= 8 + 8 sq.unite

= 16 sq. unite

Hence,our answer is 16 sq.unite

Thanks...

:)