Question

1. for the rectangle shown calculate: a) the perimeter b) the area 2\frac{2}{3} in. 4\frac{3}{4} in.

Explanation:

Step1: Convert mixed - numbers to improper fractions

$2\frac{2}{3}=\frac{2\times3 + 2}{3}=\frac{8}{3}$ and $4\frac{3}{4}=\frac{4\times4+3}{4}=\frac{19}{4}$

Step2: Calculate the perimeter of the rectangle

The formula for the perimeter $P$ of a rectangle is $P = 2(l + w)$.
$P=2(\frac{8}{3}+\frac{19}{4})$
First, find a common denominator, which is $12$.
$\frac{8}{3}+\frac{19}{4}=\frac{8\times4}{3\times4}+\frac{19\times3}{4\times3}=\frac{32}{12}+\frac{57}{12}=\frac{32 + 57}{12}=\frac{89}{12}$
$P = 2\times\frac{89}{12}=\frac{89}{6}=14\frac{5}{6}$ inches

Step3: Calculate the area of the rectangle

The formula for the area $A$ of a rectangle is $A=l\times w$.
$A=\frac{8}{3}\times\frac{19}{4}$
Cancel out common factors: $\frac{8}{3}\times\frac{19}{4}=\frac{2}{3}\times19=\frac{38}{3}=12\frac{2}{3}$ square inches

Answer:

a) $14\frac{5}{6}$ inches
b) $12\frac{2}{3}$ square inches