Question

A plot of land is in the shape of a sector of a circle of 28m.If the sectorial angle (central angle) is 60 degrees,find the area and the perimeter of the plot.​

Answer 1

Step-by-step explanation:

Answer: The area of the land is 410.67 m² and the perimeter is 85.33 m. Step-by-step explanation: The sectorial angle of the sector of the circle is 60°

bvnbcssßzfxvbhhj

plz mark me as brainliest

Answer 2

The area of the plot is 410.67 m².

The perimeter of the plot is 85.34 m.

-----------------------------------------------------------------------------------------

Let's understand a few concepts:

To calculate the area of a sector when the value of theta is given in degrees we will use the following formula:

$\boxed{\bold{Area \:of\:a\:sector= \frac{\theta}{360\°}\times \pi r^2 }}$

To calculate the length of the arc of a sector when theta is given in degrees we will use the following formula:

$\boxed{\bold{Length \:of\:arc= \frac{\theta}{360\°}\times2 \pi r }}$

-----------------------------------------------------------------------------------------

Let's solve the given problem:

The radius of the sector-shaped plot of land (r) = 28 m

The central angle (θ) = 60°

Finding the area of the sector-shaped the plot of land:

The area of the plot of land in the shape of a sector is,

= $\frac{60\°}{360\°} \times \frac{22}{7} \times 28^2$

= $\frac{1}{6} \times \frac{22}{7} \times 28^2$

= $\frac{17248}{42}$

= $\bold{410.67\:m^2}$

Finding the perimeter of the sector-shaped the plot of land:

The perimeter of the plot of land in the shape of a sector is,

= [Arc length] + [Radius] + [Radius]

= $[\frac{60\°}{360\°} \times2 \times \frac{22}{7} \times 28] + 28 + 28$

= $[\frac{1}{6} \times 2\times \frac{22}{7} \times 28}] + 56$

= $[\frac{1}{3} \times 22 \times 4}] + 56$

= $29.34 + 56$

= $\bold{85.34\:m}$

Thus, the area and the perimeter of the plot is 410.67 m² and 85.34 m respectively.

------------------------------------------------------------------------------------------

Learn more on brainly.in:

brainly.in/question/20947997

brainly.in/question/5710888