Question

the perimeter of a sector of radius 5.2cm is 16.4cm. find the area of sector​

Answer 1

Answer:

0.542

Step-by-step explanation:

o is my theta

p = 2r + ro

16.4 = 10.4 + 5.2o

6/5.2 =o

a = 0/360 *2 pi r*r

= 0.542

Answer 2

$\Large{\textbf{\underline{\underline{According\;to\;the\;Question}}}}$

Given,

$\textbf{\underline{Perimeter\;of\;sector\;of\;circle\;is\; 16.4\;cm}}$  

Also,

$\textbf{\underline{Radius\;of\;Circle\;is\;5.2 cm}}$  

Length of Arc

5.2 + 5.2 + L = 16.4

10.4 + L = 16.4

L = 16.4 - 10.4

L = 6

We get,

$\textbf{\underline{Length\;of\;Arc\;is\;6cm}}$  

Now,

Using Formula of Area of Sector

${\boxed{\sf\:{\dfrac{1}{2}\times Radius\times Length\;of\;Arc}}}$

$\rm \: \: \: \: \: \: \: \: \:=\dfrac{1}{2}\times 5.2\times 6$

$\rm \: \: \: \: \: \: \: \: \:=\dfrac{1}{\cancel{2}}\times 5.2\times \cancel{6}$

Area = 5.2 × 3

Area = 15.6 cm²