Question

A sector of radius 4.2cm has an area 9.24cm².Find its perimeter

Answer 1

Answer: perimeter of sector is 12.8 cm

Solution:

It is given that

radius r= 4.2 cm

Area of sector =
$\frac{ \theta }{360} \pi {r}^{2}$
it is given that area of sector is 9.24 cm²

$\frac{ \theta }{360°} \pi {r}^{2} = 9.24 \\ \\ \theta = \frac{9.24 \times 360 \times 7}{22 \times4.2 \times 4.2 } \\ \\ \theta = \frac{924 \times 360 \times 7}{22 \times42 \times 42 } \\ \\ \theta = 60°$
length of arc=
$\frac{ \theta }{360°} \times 2\pi r \\ \\ = \frac{60° \times 2 \times 22 \times 4.2}{360° \times 7} \\ \\ = 4.4 \: cm$
Perimeter of sector = length of arc+2r

$= 4.4 + 2(4.2) \\ \\ = 4.4 + 8.4 \\ \\ = 12.8 \: cm$

Hence perimeter of sector is 12.8 cm

Hope it helps you.

Answer 2

It is given that

radius r= 4.2 cm

Area of sector =

\begin{gathered}\frac{ \theta }{360} \pi {r}^{2} \\ \\\end{gathered}

360

θ

πr

2

it is given that area of sector is 9.24 cm²

\begin{gathered}\frac{ \theta }{360°} \pi {r}^{2} = 9.24 \\ \\ \theta = \frac{9.24 \times 360 \times 7}{22 \times4.2 \times 4.2 } \\ \\ \theta = \frac{924 \times 360 \times 7}{22 \times42 \times 42 } \\ \\ \theta = 60° \\ \\\end{gathered}

360°

θ

πr

2

=9.24

θ=

22×4.2×4.2

9.24×360×7

θ=

22×42×42

924×360×7

θ=60°

length of arc=

\begin{gathered}\frac{ \theta }{360°} \times 2\pi r \\ \\ = \frac{60° \times 2 \times 22 \times 4.2}{360° \times 7} \\ \\ = 4.4 \: cm \\ \\\end{gathered}

360°

θ

×2πr

=

360°×7

60°×2×22×4.2

=4.4cm

Perimeter of sector = length of arc+2r

\begin{gathered}= 4.4 + 2(4.2) \\ \\ = 4.4 + 8.4 \\ \\ = 12.8 \: cm \\ \\\end{gathered}

=4.4+2(4.2)

=4.4+8.4

=12.8cm