Lesson 11-6 Arc Lengths and Areas of Sectors (page 452) Essential Question How can you calculate the area of any figure?

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Lesson 11-6 Arc Lengths and Areas of Sectors (page 452) Essential Question How can you calculate the area of any figure?

Arc Lengths & Areas of Sectors

Two different numbers that describe the size of an arc are: A O B (1)the measure of the arc, ie.. (2)the arc length, which is the length of a piece of the circumference.

The arc length is a fraction of the whole circumference. The length of the arc equals the fraction times the circumference of the circle. A O B xº

A sector of a circle is a region bounded by two radii and an arc of the circle. The area of a sector is a fraction of the area of the whole circle. A O B xº

Area of a Sector The area of a sector equals the fraction times the area of the circle. A O B xº

#1 In O with radius 6 and m ∠ AOB = 150º, find the lengths of and. A O B D C 10º 150º r = 6

#1 In O with radius 6 and m ∠ AOB = 150º, find the lengths of and. A O B D C 10º 150º r = 6 200º

#2 Find the area of the shaded sector in the circle with radius equal to º r = 12

#3 Find the area of the shaded region in the circle with radius equal to º Please note: This is also referred to as the Area of a Segment.

#3 Find the area of the shaded region in the circle with radius equal to º WARNING? We do not have a formula for this figure!

#3 Find the area of the shaded region in the circle with radius equal to º

#3 Find the area of the shaded region in the circle with radius equal to º General approach: A shaded region = A big region - A small region For this problem: A shaded region = A sector - A triangle

#3 Find the area of the shaded region in the circle with radius equal to º A shaded region = A sector - A triangle r = 6

#3 Find the area of the shaded region in the circle with radius equal to º r = 6 60º 30º r = 6 h = 3 A shaded region = A sector - A triangle

#3 Find the area of the shaded region in the circle with radius equal to º r = 6 60º 30º r = 6 h = 3 A shaded region = A sector - A triangle

#3 Find the area of the shaded region in the circle with radius equal to º r = 6 60º 30º r = 6 h = 3 A shaded region = A sector - A triangle

#4 Find the area of the shaded region in the circle with radius equal to 2 inches. 300º WARNING? We do not have a formula for this figure!

#4 Find the area of the shaded region in the circle with radius equal to 2 inches. 300º

#4 Find the area of the shaded region in the circle with radius equal to 2 inches. 300º General approach: A shaded region = A region + A region For this problem: A shaded region = A sector + A triangle

#4 Find the area of the shaded region in the circle with radius equal to 2 inches. 300º A shaded region = A sector + A triangle r = 2”

#4 Find the area of the shaded region in the circle with radius equal to 2 inches. 300º r = 2” 30º 60º 2”2” A shaded region = A sector + A triangle 60º

#4 Find the area of the shaded region in the circle with radius equal to 2 inches. 300º r = 2” 30º 60º 30º 60º A shaded region = A sector + A triangle 2”2”

#4 Find the area of the shaded region in the circle with radius equal to 2 inches. 300º r = 2” 30º 60º 30º 60º A shaded region = A sector + A triangle 2”2”

Chapter 11 Project Assignment Circle Graph Activity This is due _________________! Please make this VERY nice! How can you calculate the area of any figure?

Assignment Written Exercises on pages 453 & 454 REQUIRED: 1 to 19 odd numbers How can you calculate the area of any figure? UPDATE YOUR STUDENT AID CARD!