Question

find the perimeter of each figure

Answer 1

$\huge {\mathfrak{\underline{\underline{Formula \: \colon}}}}$

Consider $\bold{\pi \: =\: 3.14}$

Perimeter of semi-circle is $\bold{(\pi r\: +\: d)}$

Perimeter of rectangle is $\bold{2(l \: + \: b)}$

Perimeter is generally $\bold{ sum \: of \: all \: sides}$

Perimeter of quadrant is $\bold{\dfrac{1}{2} \pi r \: + \: 2r}$

$\bold{\underline{\underline{Solution \: 1 }}}$

Rectangle + Semicircle

Length = 12 m

Breadth = 6 m

Diameter of Semicircle = 6 m

Radius of semicircle = 3 m

Total Perimeter = 2[l + b] + [πr + d]

$\implies 2[12\: + \: 6] \: + \: [\pi (3) \: +\: 6]$

$\implies 2[18] \: + \: [15.42]$

$\implies 36 \: + \: 15.42$

$\implies \bold{51.42 \: m}$

$\bold{\underline{\underline{Solution \: 2}}}$

Semicircle + Rectangle + Semicircle

Length = 28 cm

Radius of semicircles = 7 cm

Breadth of rectangle = Diameter of circle = 2r = 14 cm

Total Perimeter = 2[l + b] + 2[ πr + d]

$\implies 2[ 28 \: + \: 14] \: + \: 2[\pi (7) \: + \: 14 ]$

$\implies 2[ 42] \: + \: 2[\pi (7) \: + \: 14 ]$

$\implies 2[42]\: + \: 2[35.99]$

$\implies 84 \: + \: 71.98$

$\implies \bold{155.98 \: cm}$

$\bold{\underline{\underline{Solution \: 3}}}$

Radius of quadrant = 21 m

Perimeter of given quadrant is

$\implies \bold{\dfrac{1}{2} \pi 21 \: + \: 2(21)}$

$\implies \bold{\dfrac{1}{2} \times \dfrac{22}{7} \times 21 \: + \: 2(21)}$

$\implies \bold{( 11 \times 3) + \: 42}$

$\implies \bold{ 33 \: + \: 42}$

$\implies \bold{ 75 \: m}$

$\bold{\underline{\underline{Solution \: 4 }}}$

Total perimeter = Perimeter of triangle + Perimeter of semicircle

Perimeter of triangle = sum of all sides

$\implies \bold{14\: + \: 21 \: + \: 21}$

$\implies \bold{14\: + \: 42}$

$\implies \bold{56\: cm}$

Perimeter of semicircle = $\bold{(\pi (7)\: +\: 14)}$

= $\bold{(\dfrac{22}{7} \times 7 \: +\: 14)}$

= $\bold{22\: + \: 14}$

= $\bold{36\: cm}$

Total perimeter = (56 + 36) cm

Now total perimeter of given diagram is $\bold{92\: cm}$.

$\bold{\underline{\underline{Solution \: 5}}}$

Total Perimeter = Perimeter of circle - Perimeter of quadrant

Radius of circle = 2.1 m

Diameter of circle = 2 × 2.1

= 4.2 m

Total perimeter = 2πr - $\bold{\dfrac{1}{2} \pi r \: + \: 2r}$

$\implies 2\times \dfrac{22}{7} \times 2.1 - \bold{\dfrac{1}{2}\times \dfrac{22}{7} \times 2.1 \: + \: 2\times (2.1)}$

$\implies 13.2 \: - 7.5 \:$

$\implies 5.7 \: m\:$

$\bold{Thanks}$

Answer 2

Step-by-step explanation:

(a) 51.42cm²

(b) 155.98cm²

(c) 75cm²

(d) 92cm²

(e) 5.7cm²