Question

1. Find the perimeter of the following. (Take a = 3.14)
b.
a.​

Answer 1

Answer:

(a) 29 cm

(b) 61.68 cm

Step-by-step explanation:

(a) It is a sector.

radius = 9 cm

length of the arc = 11 cm

      $\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\put(-2.3,0){\line(1,-1){2.3}}\put(2.3,0){\line(-1,-1){2.3}}\put(-2.5,-0.4){\sf P}\put(2.3,-0.4){\sf Q}\put(-0.1,-2.7){\sf R}\put(-1.3,-0.9){\sf 9 cm}\put(0.5,-0.9){\sf 9 cm}\end{picture}$

Perimeter of the sector = 2(radius) + length of the arc

⇒ Perimeter of the sector = 2(9 cm) + 11 cm

⇒ Perimeter of the sector = 18 cm + 11 cm

⇒ Perimeter of the sector = 29 cm

∴ The perimeter of the sector is 29 cm

(b) It is a semicircle.

radius = 12 cm

  $\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\put(-2.3,0){\line(1,0){4.6}}\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\put(-2.3,-0.2){\vector(1,0){2.4}}\put(0.1,-0.2){\vector(-1,0){2.4}}\put(-1.5,-0.6){\sf 12 cm}\put(0.1,0){\circle*{0.13}}\end{picture}$

Perimeter of the semicircle = half the circumference of the circle + diameter

Perimeter of the semicircle = πr + 2r

⇒ Perimeter of the semicircle = (3.14)(12) + 2(12)

⇒ Perimeter of the semicircle = 37.68 + 24

⇒ Perimeter of the semicircle = 61.68 cm

∴ The perimeter of the semicircle is 61.68 cm

Answer 2

Step-by-step explanation:

$\huge\sf\underline\blue{answer}$

1) perimeter of diamond = sum of all sides

= PQ+QR+PR

= 11cm+9cm+9cm

= 29cm

2) perimeter of semi circle = πr/2

= 3.14×(12cm/2

= 3.14×6cm

= 18.84cm