X5) A B C D E F GH is a regular octagon inscribed in
I a circle of radius 1 unit o is centre of
- circle find
Lil.Radian measure of LOOB
i e (chord no) iii) e Carc AB
in area of region enclosed beth chord no
arc AB
Answers
Answer:
The radian measure of ∠AOB = π/4 rad
Length of Chord AB = √2 units = 1.414 units
Length of Arc AB = 0.785 units
Area of the segment = 0.0391 square units
Step-by-step explanation:
Given Data:
ABCDEFGH is a regular octagon.
Radius of the circle, R = 1 unit
To find: radian measure of ∠AOB, length of chord AB, length of arc AB and Area of region enclosed between chord AB and arc AB.
Step 1: finding the radian measure of angle AOB
In regular octagon, n = 8
Since ABCDEFGH is a regular octagon, therefore, the centre angle is given as,
θ = Angle AOB = 360° / 8 = 45° = 45° * π/180° = π/4 rad
Step 2: finding the length of chord AB
R = OA = OB = 1 unit
Consider ∆AOB(from figure given below), by using Pythagoras theorem, we get
Length of chord AB = √[OA² + OB²] = √[1² + 1²] = √2 units
Step 3: finding the length of arc AB
If θ is measured in radians then the arc length of AB i.e., “s” is given as,
s = r * θ = 1 cm * π/4 rad = 0.785 units
Step 4: finding the area of the region enclosed between chord AB and arc AB
The area enclosed between the chord AB and arc AB is known as the segment.
Therefore,
Area of the segment (considering θ in degrees)
= R² / 2 [(π/180)θ – sin θ]
= (1)² / 2 [(π/180)45° – sin45° ]
= ½ * [0.785 – 0.707]
= 0.078 / 2
= 0.0391 square units
