Question

I need help doing this... I’m totally lost

Answer 1

`-(a+1(3)/(4)b)`

Explanation:

Perimeter of a polygon = Sum of the measures of all sides of the polygon

For the given trapezoid,

Perimeter =
`1(1)/(2)a+1(1)/(2)b+1(1)/(2)a+2(3)/(4)b`

By combining similar terms,

Perimeter =
`(1(1)/(2)+1(1)/(2))a+(1(1)/(2)+2(3)/(4))b`

=
`(1+(1)/(2)+1+(1)/(2))a+(1+(1)/(2)+2+(3)/(4))b`

= (2 + 1)a +
`(3+(1)/(2)+(3)/(4))b`

= 3a +
`(3+(2)/(4)+ (3)/(4))b`

= 3a +
`(3+(5)/(4))b`

= 3a +
`(3+1+(1)/(4))b`

= 3a +
`4(1)/(4)b`

For rectangle,

Perimeter = 2(Length + Width)

= 2(2a + 3b)

Difference between the perimeter of trapezoid and rectangle,

= (3a +
`4(1)/(4)b`) - 2(2a + 3b)

= (3a - 4a) + (
`4(1)/(4)b` - 6b)

= -a +
`(4+(1)/(4)-6)b`

= -a +
`((1)/(4)-2)b`

= -a +
`((1)/(4)-(8)/(4))b`

= -a -
`(7)/(4)b`

=
`-(a+1(3)/(4)b)`