The area of the shape (quadrilateral) is 16 square units.
Explanation:
The given four sides of quadrilateral = (1,3), (5,3), (7,-1) and (1,-1)
To find, the area of the shape (quadrilateral) = ?
We know that,
The area of quadrilateral =
![(1)/(2) [x_(1)( y_(2)-y_(3))+x_(2)( y_(3)-y_(4))+x_(3)( y_(4)-y_(1))+x_(4)( y_(1)-y_(2))]](https://img.qammunity.org/2021/formulas/mathematics/high-school/2hpo1j2x4ehkkuirlz0660t94llxckyp8g.png)
=
![(1)/(2) [1( 3+1)+5( -1+1)+7( -1-3)+1}( 3-3)]](https://img.qammunity.org/2021/formulas/mathematics/high-school/e3k8z80khpx0oc2qm1510q5jtnsys64kxv.png)
=
![(1)/(2) [1(4)+5( 0)+7( -4)+1}( 0)]](https://img.qammunity.org/2021/formulas/mathematics/high-school/5kj1lij5xezm9icalysw5cjf2zbmixt20e.png)
=
![(1)/(2) [4+0-28+0]](https://img.qammunity.org/2021/formulas/mathematics/high-school/gexlf6spoxdtsix6f55j6tw5rkoww6miio.png)
=
![(1)/(2) [32]](https://img.qammunity.org/2021/formulas/mathematics/high-school/zzr6f8hd5gptnm985dylvcwb88cc3nkojl.png)
= 16 square units.
Thus, the area of the shape (quadrilateral) is 16 square units.