Question

Find the perimeter quickly I will give 25 point5 the question and the mivelenious one

Answer 1

Answer:

Step-by-step explanation:

Question (5)

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

AP = AR = 7 cm

Formula to get the length of arc(PQR) = $\frac{\theta}{360}(2\pi r)$

Here, r = radius of the sector

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

arc(PQR) = $\frac{45}{360}(2\pi )(7)$

               = $\frac{630\pi }{360}$

               = $\frac{7\pi }{4}$

               = 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) = $\frac{\theta}{360}(2\pi r)$

               = $\frac{45}{360}(2\pi )(3.5)$

               = 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 + $\frac{\theta}{360}(2\pi r)$

= 42 + $\frac{(360-120)}{360}(2\pi )(21)$

= 42 + 28π

= 42 + 87.96

= 129.96

≈ 130 cm