Question

The perimeter of a certain sector of a circle of radius 6.5 cm is 21cm. find the area of the sector​

Answer 1

Answer:

$the \: area \: of \: the \: sector \: is \: {58.5cm}^{2}$

NOTE: Refer to the diagram for more information

Step-by-step explanation:

$given$

$radius = 6.5cm$

$let \: o \: be \: the \: center \: of \: th e \: circle \: with \: radius 6.5cm \: nd \: oacbo \: be \: it \: ector \: with \: perimeter \: 31cm \:$

$thus \: we \: have$

$oa + ob + arc \: ab = 31cm$

$6.5 + 6.5 + arc \: ab = 31cm$

$arc \: ab = 18cm$

$now$

$area \: of \: the \: sector \: oacbo$

$\frac{1}{2} \times radius \times arc$

$\frac{1}{2} \times 6.5 \times 18$

${58.5cm}^{2}$