Answer:
[tex]-(a+1\frac{3}{4}b)[/tex]
Step-by-step explanation:
Perimeter of a polygon = Sum of the measures of all sides of the polygon
For the given trapezoid,
Perimeter = [tex]1\frac{1}{2}a+1\frac{1}{2}b+1\frac{1}{2}a+2\frac{3}{4}b[/tex]
By combining similar terms,
Perimeter = [tex](1\frac{1}{2}+1\frac{1}{2})a+(1\frac{1}{2}+2\frac{3}{4})b[/tex]
= [tex](1+\frac{1}{2}+1+\frac{1}{2})a+(1+\frac{1}{2}+2+\frac{3}{4})b[/tex]
= (2 + 1)a + [tex](3+\frac{1}{2}+\frac{3}{4})b[/tex]
= 3a + [tex](3+\frac{2}{4}+ \frac{3}{4})b[/tex]
= 3a + [tex](3+\frac{5}{4})b[/tex]
= 3a + [tex](3+1+\frac{1}{4})b[/tex]
= 3a + [tex]4\frac{1}{4}b[/tex]
For rectangle,
Perimeter = 2(Length + Width)
= 2(2a + 3b)
Difference between the perimeter of trapezoid and rectangle,
= (3a + [tex]4\frac{1}{4}b[/tex]) - 2(2a + 3b)
= (3a - 4a) + ([tex]4\frac{1}{4}b[/tex] - 6b)
= -a + [tex](4+\frac{1}{4}-6)b[/tex]
= -a + [tex](\frac{1}{4}-2)b[/tex]
= -a + [tex](\frac{1}{4}-\frac{8}{4})b[/tex]
= -a - [tex]\frac{7}{4}b[/tex]
= [tex]-(a+1\frac{3}{4}b)[/tex]
