Question

find the area of a sector whose perimeter is 64 cm and length of the arc is 44 cm ?

Answer 1

Answer:

220 cm²

Step-by-step explanation:

Perimeter = r + r + l

Where, r stands for radius and l stands for arc length.

Perimeter = 2r + l

Perimeter = 2r + 44 = 64

⇒ 2r = 64 - 44

⇒ 2r = 20

⇒ r = 20/2 = 10 cm

Now we know the formula of calculating arc length.

$Arc\: Length = \dfrac{ \theta}{360} \times 2 \pi r$

⇒ 44 cm = ( Ф / 360 ) × 2 × 22/7 × 10

⇒ 44 cm = ( Ф / 360 ) × 440/7

⇒ Ф = 44 × 7 × 360 / 440 = 110880 / 440 = 252°

Therefore Ф = 252°

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

Substituting the values we get,

⇒ Area of Sector = ( 252 / 360 ) × 22/7 × 10 × 10

⇒ Area of Sector = ( 252 / 360 ) × 2200 / 7 = 554400 / 2520 = 220 cm²

Therefore Area of the sector is 220 cm².