Question

The area of semi circle 27.72 cm^2 find its perimeter

Answer 1

AREA of FULL CIRCLE=πr² (Here r=radius)
So SEMI CIRCLE is half of full circle
So it's area=
$\frac{1}{2}\pi {r}^{2}$
But ACTUAL area=27.72 cm²

Using formula
$area = \frac{1}{2}\pi {r}^{2} \\ \frac{1}{2} \pi {r}^{2} = 27.72 \\ (value \: of \: \pi = \frac{22}{7} ) \\ \frac{1}{2} \times \frac{22}{7} \times {r}^{2} = 27.72 \\ {r}^{2} = 27.72 \times \frac{7}{22} \times \frac{2}{1} \\ {r}^{2} = 17.64 \\ r = \sqrt{17.64} \\ r = 4.2 cm \\ \\ so \: radius = 4.2 \: cm$
Perimeter of circle is CIRCUMFERANCE
CIRCUMFERANCE of FULL CIRCLE=2πr
CIRCUMFERANCE of HALF CIRCLE=2πr/2

$\frac{2\pi \: r \: }{2} \\ \frac{2 \times 22 \times 4.2}{7 \times 2} \\ \\ \frac{184.8}{14} \\ = 13.2 \\ circumference \: or \: perimeter \\ = 13.2cm$

Answer 2

Answer:

21.6 cm

Step-by-step explanation:

Here Area of Semi-Circle given = 27.72 cm²

But we know that Area of Circle = π(radius)²

∴ Area of Semi-circle = π (radius)² /2

∴ π (radius)²/2 = 27.72

[Putting value of π =22/7 and transposing values to other side]

radius² = (27.72 × 2 × 7)/22    

radius² = 17.64

Radius² = (4.2)²

radius = 4.2 cm  -------- ( i )

Now

We know that circumference of the circle = 2π×radius

∴ circumference of semi circle = π × radius

Observe the attached figure. You can see that

Perimeter of Semi Circle = Half Circumference of Circle + Diameter

∴ Perimeter of Semi Circle = π × radius + 2 × radius [∵diameter = 2 × radius]

Putting values of π and radius

                      = (22 × 4.2)/7  + 2 × 4.2

                      = 22 × 0.6 + 8.4

                      = 13.2 + 8.4

                       = 21.6 cm

∴ Perimeter of Semi Circle  = 21.6 cm

Note: A semi circle is not an open curve. It is always enclosed by Length of Arc and Diameter. A semi Circle without diameter is just an Arc which holds no definite area (because its open). So, if Area of semi circle is given and perimeter is asked, just consider the figure which I have attached with the solution. :)