Question

Find the perimeter quickly I will give 25 point
5 the question and the mivelenious one

Answer 1

Explanation:

Question (5)

Perimeter of sector APQR = AP + arc(PQR) + AR

AP = AR = 7 cm

Formula to get the length of arc(PQR) =
`(\theta)/(360)(2\pi r)`

Here, r = radius of the sector

θ = Angle by the arc PQR at the center of the circle

arc(PQR) =
`(45)/(360)(2\pi )(7)`

=
`(630\pi )/(360)`

=
`(7\pi )/(4)`

= 4.497 ≈ 4.50 cm

Perimeter of APQR = 2(7) + 4.50

= 18.50 cm

Perimeter of shaded region = BP + arc(BCD) + arc(PQR) + DR

arc(BCD) =
`(\theta)/(360)(2\pi r)`

=
`(45)/(360)(2\pi )(3.5)`

= 0.875π

≈ 2.75 cm

Perimeter of shaded region = 2(3.5) + 2.75 + 4.50

= 14.25 cm

Difference in perimeter of APQR and perimeter of shaded region = 18.50 - 14.25

= 4.25 cm

Perimeter of APQR is 4.25 cm more than the perimeter of the shaded region.

Miscellaneous question

Perimeter of remaining lamina = 2(21) + Length of arc of the remaining portion

= 42 +
`(\theta)/(360)(2\pi r)`

= 42 +
`((360-120))/(360)(2\pi )(21)`

= 42 + 28π

= 42 + 87.96

= 129.96

≈ 130 cm