Question

find the area of the figure to the nearest tenth

Answer 1

Solution :

Area of Sector = $\dfrac{\theta}{360^{\degree}}\times\pi\times r^{2}$

Now given is angle $\theta$ = 165°

Radius be 7 inches

Now formula of sector for area

Area of Sector = $\dfrac{165^{\degree}}{360^{\degree}}\times\pi\times 7^{2}$

Area of Sector = $\dfrac{165^{\degree}}{360^{\degree}}\times 3.14 \times 49$

Area of Sector = $0.45 \times 3.14 \times 49$

Area of given figure is 70.7 in²

Answer 2

ANSWER:

Given figure is a sector

Angle = 165°

Radius = 7 inch

$\small \rm{area \: of \: sector}\begin{cases} \rm{formula1 : \frac{1}{2 } {r}^{2} \theta } \\ \\ \rm{formula2 :\frac{\pi {r}^{2} \theta }{ 360} } \end{cases}$

About Formula 1 :

→ θ is measured in radians

About Formula 2 :

→ θ is measured in degrees

Using formula no. 1:

★ 1/2 r²θ

θ is measured in radians so 165° should be converted to radians

Using formula

D/90 = 2c/π

D = 165°

→ c = 165π/180

→ c = 11π/12

Substituting we get

$\dagger \: \: \: \dfrac{1}{2} \times {7}^{2} \times \dfrac{11\pi}{12} \\ \\ \dag \: \: \: \frac{49(11\pi)}{24} = \frac{539\pi}{24} \\ \\ \dag \: \: \: \dfrac{ \cancel{539} \times \dfrac{22}{ \cancel7} }{24} = \frac{1694}{24} = 70.7 \: \rm{in}^{2}$

Using formula no.2:

$\small \to \dfrac{\pi \times {7}^{2} \times 165}{180} = \dfrac{ \frac{22}{ \cancel7} \times {7}^{ \cancel2} \times \cancel{165} }{ \cancel{180}} \\ \\ \small \to \frac{1694}{24} = 70.7 \: \: \rm{in}^{2}$

Hence , area of given sector is 70.7 inch²