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In circle L, with [tex]m\angle KLM = 42^\circ[/tex] and [tex]KL = 13[/tex], find the area of sector KLM. Round to the nearest hundredth.

Answer :

To find the area of sector [tex]KLM[/tex] in circle [tex]L[/tex], we can use the formula for the area of a sector:

[tex]\text{Area of sector} = \frac{\theta}{360} \times \pi \times r^2[/tex]

Where:

  1. [tex]\theta[/tex] is the central angle in degrees.
  2. [tex]r[/tex] is the radius of the circle.

Given that [tex]m\angle KLM = 42^\circ[/tex] and [tex]KL = 13[/tex], we can determine that the radius [tex]r[/tex] of the circle is [tex]13[/tex].

Let's substitute these values into the formula:

[tex]\text{Area of sector} = \frac{42}{360} \times \pi \times 13^2[/tex]

[tex]\text{Area of sector} = \frac{42}{360} \times \pi \times 169[/tex]

[tex]\text{Area of sector} = \frac{42}{360} \times 531.441[/tex]

[tex]\text{Area of sector} = \frac{42}{360} \times 531.441 \approx 61.94[/tex]

Therefore, the area of sector [tex]KLM[/tex] is approximately [tex]61.94[/tex] square units, rounded to the nearest hundredth.

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Rewritten by : Barada

To find the area of sector [tex]KLM[/tex] in circle [tex]L[/tex], we need to use the formula for the area of a sector:

[tex]\text{Area of sector} = \frac{\theta}{360} \times \pi r^2[/tex]

Where:

  • [tex]\theta[/tex] is the central angle of the sector in degrees.
  • [tex]r[/tex] is the radius of the circle.

In this problem:

  • [tex]\theta = 42^\circ[/tex]
  • [tex]r = 13[/tex]

Plug these values into the formula:

[tex]\text{Area of sector} = \frac{42}{360} \times \pi \times (13)^2[/tex]

First, calculate [tex]13^2[/tex]:

[tex]13^2 = 169[/tex]

Now, substitute the value back into the formula:

[tex]\text{Area of sector} = \frac{42}{360} \times \pi \times 169[/tex]

Simplify [tex]\frac{42}{360}[/tex]:

[tex]\frac{42}{360} = \frac{7}{60}[/tex]

Now the expression becomes:

[tex]\text{Area of sector} = \frac{7}{60} \times \pi \times 169[/tex]

Using [tex]\pi \approx 3.14159[/tex], the expression is:

[tex]\text{Area of sector} \approx \frac{7}{60} \times 3.14159 \times 169[/tex]

Carry out the multiplication:

[tex]\approx \frac{7}{60} \times 531.25331[/tex]

[tex]\approx 62.08331[/tex]

So, the area of sector [tex]KLM[/tex] is approximately [tex]62.08[/tex] square units when rounded to the nearest hundredth.