Question

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

Answer 1

Answer:

$-(a+1\frac{3}{4}b)$

Step-by-step explanation:

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

For the given trapezoid,

Perimeter = $1\frac{1}{2}a+1\frac{1}{2}b+1\frac{1}{2}a+2\frac{3}{4}b$

By combining similar terms,

Perimeter = $(1\frac{1}{2}+1\frac{1}{2})a+(1\frac{1}{2}+2\frac{3}{4})b$

                 = $(1+\frac{1}{2}+1+\frac{1}{2})a+(1+\frac{1}{2}+2+\frac{3}{4})b$

                 = (2 + 1)a + $(3+\frac{1}{2}+\frac{3}{4})b$

                 = 3a + $(3+\frac{2}{4}+ \frac{3}{4})b$

                 = 3a + $(3+\frac{5}{4})b$

                 = 3a + $(3+1+\frac{1}{4})b$

                 = 3a + $4\frac{1}{4}b$

For rectangle,

Perimeter = 2(Length + Width)

                 = 2(2a + 3b)

Difference between the perimeter of trapezoid and rectangle,

= (3a + $4\frac{1}{4}b$) - 2(2a + 3b)

= (3a - 4a) + ($4\frac{1}{4}b$ - 6b)

= -a + $(4+\frac{1}{4}-6)b$

= -a + $(\frac{1}{4}-2)b$

= -a + $(\frac{1}{4}-\frac{8}{4})b$

= -a - $\frac{7}{4}b$

= $-(a+1\frac{3}{4}b)$