A wire bent in the form of a semi circle encloses an area of 7700cm2. If the same wire is bent into a square, calculate the area enclosed by the square

please hurry and answer fast..thank uuu so much

Answer: 8100 cm2

Step-by-step explanation:

First find radius

Area of semi circle = Pi*r2 / 2

7700 = 22/7 * r2/2

r2 = 7700 * 7 * 2 / 22

r2 = 700 * 7

r = square root of 7*7*10*10 ( I converted 700 into simpler numbers)

r = 7 x 10

r = 70 cm

Perimeter = r(Pi + 2)

= 70 ( 22/7 + 14/7)

= 70 * 36/7

= 360 cm

Let us take side of square as “x”

4x = 360

x = 360 / 4

x = 90

Area of square = side * side

= 90 * 90

= 8100 cm2

A semicircle is simply the half of a complete circle, and it can be gotten by dividing the circle through its center into equal halves.

The area of the enclosed square wire is 3025 square meters

The given parameters are:

[tex]\mathbf{Area= 7700cm^2}[/tex]

The area of a semicircle is

[tex]\mathbf{Area= \frac{\pi r^2}{2}}[/tex]

Substitute 7700 for Area

[tex]\mathbf{\frac{\pi r^2}{2} = 7700}[/tex]

Express pi as 22/7

[tex]\mathbf{\frac{22 \times r^2}{7 \times 2} = 7700}[/tex]

Divide through by 22

[tex]\mathbf{\frac{r^2}{7 \times 2} = 350}[/tex]

Multiply both sides by 14

[tex]\mathbf{r^2 = 4900}[/tex]

Take square roots of both sides

[tex]\mathbf{r = 70}[/tex]

Next, calculate the circumference of the semicircle

[tex]\mathbf{C = \pi r}[/tex]

So, we have:

[tex]\mathbf{C = \frac{22}{7} \times 70}[/tex]

[tex]\mathbf{C = 220}[/tex]

This means that the length of the wire is 220 meters.

This also represents the perimeter of the square.

The perimeter of the square is calculated using:

[tex]\mathbf{P = 4L}[/tex]

Where L represents the side length

So, we have:

[tex]\mathbf{4L = 220}[/tex]

Divide both sides by 4

[tex]\mathbf{L = 55}[/tex]

The area of the enclosed square is then calculated using:

[tex]\mathbf{Area = L^2}[/tex]

So, we have:

[tex]\mathbf{Area = 55^2}[/tex]

Evaluate the square

[tex]\mathbf{Area = 3025}[/tex]

Hence, the area of the enclosed square wire is 3025 square meters

Read more about areas at:

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