How do you find the arc length and area of a sector?

How to find the length of an arc and sector area: an example

Decide on the radius of your circle.
What will be the angle between the ends of the arc?
Calculate the arc length according to the formula above: L = r * θ = 15 * π/4 = 11.78 cm .
Calculate the area of a sector: A = r² * θ / 2 = 15² * π/4 / 2 = 88.36 cm² .

What is the formula for arc length of a sector?

Multiply the sector area by 2 and further, divide the result by the central angle in radians. Find the square root of the result of the division. Multiply this obtained root by the central angle again to get the arc length. The units of this calculated arc length will be the square root of the sector area units.

How do you find the area of a sector with the arc?

If the central angle measures 60 degrees, divide the 360 total degrees in the circle by 60. Multiply this by the measure of the corresponding arc to find the total circumference of the circle. Use the circumference to find the radius, then use the radius to find the area.

What is arc length and sector area?

A radius of a circle a straight line joining the centre of a circle to any point on the circumference. The arc length formula is used to find the length of an arc of a circle; ℓ=rθ ℓ = r θ , where θ is in radian. Sector area is found A=12θr2 A = 1 2 θ r 2 , where θ is in radian.

How do you find the degree of an arc?

An arc measure is an angle the arc makes at the center of a circle, whereas the arc length is the span along the arc. This angle measure can be in radians or degrees, and we can easily convert between each with the formula π radians = 180° π r a d i a n s = 180 ° .

How to calculate arc length and sector area?

This Complete Guide to Arc Length and Sector Area includes several examples, a step-by-step tutorial, an animated video mini-lesson, and a free equation of a circle worksheet and answer key. *This lesson guide accompanies our animated Arc Length and Sector Area Explained! video. Want more free math lesson guides and videos?

How to calculate the length of Arc KL?

Answer: The length of Arc KL is approximately 25.1cm (and 8π if you want to leave your answer in terms of pi). Notice that this question is asking you to find the area of a sector of circle K, so you will have to use the Sector Area Formula to solve it!

What are the properties of the arc length equation?

Before you learn the arc length equation and the area of a sector equation, let’s quickly review two very important (and very familiar) circle properties: Circumference and Area The circumference of a circle is the linear distance around the circle, or the length of the circle if it were opened up and turned into a straight line.

How to calculate the ARA of the Green sector?

Simplify the numerator, then divide. Answer: The ara of the green sector is approximately 4.4 square cm (and (35/8)π if you want to leave your answer in terms of pi). Still confused? Check out the animated video lesson below:

How do you find the arc length and area of a sector? How to find the length of an arc and sector area: an example Decide on the radius of your circle. What will be the angle between the ends of the arc? Calculate the arc length according to the formula above: L = r…