Find the area of the shaded region.
Problem 1 :
The diagram shows an equilateral triangle ABC with sides of length 6 cm.
P is the midpoint of AB.
Q is the midpoint of AC.
APQ is a sector of a circle, center A.
Calculate the area of the shaded region.
Give your answer correct to 3 significant figures.
Solution:
So, area of the shaded region is 10.878 cm^{2}.
Problem 2 :
The diagram shows a sector OABC of a circle with centre O.
OA = OC = 10.4 cm
Angle AOC = 120˚
(a) Calculate the length of the arc ABC of the sector. Give your answer correct to 3 significant figures.
(b) Calculate the area of the shaded segment ABC . Give your answer correct to 3 significant figures.
Solution:
a)
The length of arc ABC:
Arc length = 2πr (θ/360°)
= 2 × 3.14 × 10.4(120°/360°)
= 21.771 cm
b)
The area of shaded segment ABC,
Problem 3 :
The diagram shows a sector of a circle with centre O.
The radius of the circle is 8 cm.
PRS is an arc of the circle.
PS is a chord of the circle.
Angle POS = 40˚
Calculate the area of the shaded segment.
Give your answer correct to 3 significant figures.
Solution:
Hence, area of shaded region is 1.752 cm^{2}.
Problem 4 :
ABC is an arc of a circle centre O with radius 80 m.
AC is a chord of the circle.
Angle AOC = 35˚.
Calculate the area of the shaded region.
Give your answer correct to 3 significant figures.
Solution:
Hence, area of shaded region is 118.756 m^{2}.
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