Question

Find the central angle and area of palm leaf fan radius 10.5 cm perimeter is 43 cm

Answer 1

Answer:

           The Area of the Fan is 115.5 cm² and the angle is 120 degrees.

Step-by-step explanation:

Perimeter of Fan = 43cm

Radius of Fan = 10.5 cm

Formula:

                    Perimeter = Length(l) × 2Radius(r)

To find the Length of the Arc ( l):

43 = l × 2(10.5)

43 =l × 21

Length (l) = 43-21 = 22 cm

Formula: For Angle of the Fan arc :

$Length of the Arc (l) =\frac{Angle of the Arc(\alpha)}{360}*(2\pi r)\\22 =\frac{\alpha}{360}*(2*\frac{22}{7}*10.5)\\Angle (\alpha) of \ the \ arc = \frac{360}{3}=120\ degrees$

Formula:  For Area of the fan:

Area Of the Fan(A)=  (Length×Radius )/2

$Area(A)=\frac{lr}{2}\\ =\frac{22*10.5}{2}\\ Area \ of \ the \ Fan(A)=115.5 cm^2$

Hope u find it helpful :)

Answer 2

Answer:

The Area of the Fan is 115.5 cm² and the angle is 120 degrees.

Step-by-step explanation:

Perimeter of Fan = 43cm

Radius of Fan = 10.5 cm

Formula:

Perimeter = Length(l) × 2Radius(r)

To find the Length of the Arc ( l):

43 = l × 2(10.5)

43 =l × 21

Length (l) = 43-21 = 22 cm

Formula: For Angle of the Fan arc :

\begin{gathered}Length of the Arc (l) =\frac{Angle of the Arc(\alpha)}{360}*(2\pi r)\\22 =\frac{\alpha}{360}*(2*\frac{22}{7}*10.5)\\Angle (\alpha) of \ the \ arc = \frac{360}{3}=120\ degrees\end{gathered}

LengthoftheArc(l)=

360

AngleoftheArc(α)

∗(2πr)

22=

360

α

∗(2∗

7

22

∗10.5)

Angle(α)of the arc=

3

360

=120 degrees

Formula: For Area of the fan:

Area Of the Fan(A)= (Length×Radius )/2

\begin{gathered}Area(A)=\frac{lr}{2}\\ =\frac{22*10.5}{2}\\ Area \ of \ the \ Fan(A)=115.5 cm^2\end{gathered}

Area(A)=

2

lr

=

2

22∗10.5

Area of the Fan(A)=115.5cm

2