Question

Find the area of the sector whose length of the arc is 58 cm. and the radius is 10 cm.​.​

Answer 1

Aɴsᴡᴇʀ:

• The area of the sector = 290 cm²

Gɪᴠᴇɴ:

• The length of the sector = 58 cm.
• The radius of the sector = 10 cm.

Nᴇᴇᴅ Tᴏ Fɪɴᴅ:

• The area of the sector = ?

Solution:

Fᴏʀᴍᴜʟᴀ ᴜsᴇᴅ ʜᴇʀᴇ:

• Area of sector = radius/2 × Length of arc

Pᴜᴛᴛɪɴɢ ᴛʜᴇ ᴠᴀʟᴜᴇs

➦ Area of sector = 10/2 × 58

➦ Area of sector = 10 × 29

➦ Area of sector = 290 cm²

Tʜᴇʀᴇғᴏʀᴇ:

• The area of the sector is 290 cm².

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Answer 2

AnswEr :

Area of the sector = 290 cm²

explanation :-

We're given with the radius as well as length of the sector, that is,

• Length of the sector = 58 cm.
• Radius of the sector = 10 cm.

Now,

As we're given with length of the sector and radius of the sector we know the required formula, that is,

$\begin{gathered}: \implies \sf \: \: Area = \dfrac{r}{2} \times Length \: of \: arc \\\end{gathered}$

substituting the value ,

$\begin{gathered}: \implies \sf \: \: Area = \dfrac{10}{2} \times 58 \\ \\ \\ : \implies \sf \: \: Area = 10 \times 29 \\ \\ \\ : \implies \sf \: \: { \boxed{ \sf{ \red{Area = 290 \: {cm}^{2} }}}} \: \\ \\\end{gathered}$

therefore,

area of the sector is 290 cm².

Additional information :

• Area of Sector = θ × π 360 × r²
• Area of Segment = ( θ × π 360 − sin(θ)2 ) × r²
• L = θ × π180 × r

In above formula's the value of θ is in degrees.