Question

Find the area of the shape (1,3) (5,3) (7,-1) (1,-1)

Answer 1

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))]`

=
`(1)/(2) [1( 3+1)+5( -1+1)+7( -1-3)+1}( 3-3)]`

=
`(1)/(2) [1(4)+5( 0)+7( -4)+1}( 0)]`

=
`(1)/(2) [4+0-28+0]`

=
`(1)/(2) [32]`

= 16 square units.

Thus, the area of the shape (quadrilateral) is 16 square units.