1. We can work this out without a calculator.
A chord of a circle is subtended
by an angle of x degrees.
The radius of the circle is 6√2.
What is the area of the segment
Made with angle x?
We can work this out without a calculator.
We can because we know about surds.
Diagram not
drawn to scale!!

2. Use surds and do not evaluate your answer.
A chord of a circle is the hypotenuse of an
isosceles right triangle whose legs are the
radii of the circle.
The radius of the circle is 6 √ 2.
What is the area of the triangle?
Use surds and do not evaluate your answer.

3. (6 √ 2) x (6 √ 2)  2 = Area Now you can evaluate (36 x 2)  2 = 36
A chord of a circle is the hypotenuse of an
isosceles right triangle whose legs are the
radii of the circle.
The radius of the circle is 6 √ 2.
What is the area of the triangle?
(6 √ 2) x (6 √ 2)  2 = Area
(36 x 2)  2 = 36
Now you can
evaluate

4. Find Area of circle using surds and keep your answer in terms of π
A chord of a circle is the hypotenuse of an
isosceles right triangle whose legs are the
radii of the circle.
The radius of the circle is 6 √ 2.
What is the area of the segment?
Hint!
Find Area of circle using surds and keep your answer in terms of π

5. Area = rxrxπ A = 6 √ 2 x 6 √ 2 π A = 36 x 2 π = 72π
A chord of a circle is the hypotenuse of an
isosceles right triangle whose legs are the
radii of the circle.
The radius of the circle is 6 √ 2.
What is the area of the circle ?
Area = rxrxπ
A = 6 √ 2 x 6 √ 2 π
A = 36 x 2 π = 72π

6. Area of C = 72π Segment = x72 π Segment = 18 π
A chord of a circle is the hypotenuse of an
isosceles right triangle whose legs are the
radii of the circle.
The radius of the circle is 6 √ 2.
What is the area of the segment?
Area of C = 72π
Segment = x72 π
Segment = 18 π

7. Remember A = 72 π Diagram not drawn to scale!!
A chord of a circle is the side of an
equilateral triangle and equal to the
radius of the circle.
The radius of the circle is 6 √ 2.
What is the area of the segment?
Remember
A = 72 π
Diagram not
drawn to scale!!

8. A = 72 π Segment = x72 π Segment = 12 π Diagram not drawn to scale!!
A chord of a circle is the side of an
equilateral triangle and equal to the
radius of the circle.
The radius of the circle is 6 √ 2.
What is the area of the segment?
A = 72 π
Segment = x72 π
Segment = 12 π
Diagram not
drawn to scale!!

9. Remember A = 72 π Diagram not drawn to scale!!
A chord of a circle is subtended
by an angle of x degrees.
The radius of the circle is 6 √ 2.
What is the area of the segment made with angle x?
Remember
A = 72 π
Diagram not
drawn to scale!!

10. A = 72 π segment = x/360 X 72 π Segment = x/5 X π Segment = x π/5
A chord of a circle is subtended
by an angle of x degrees.
The radius of the circle is 6 √ 2.
What is the area of the segment?
A = 72 π
segment = x/360 X 72 π
Segment = x/5 X π
Segment = x π/5
Diagram not
drawn to scale!!

11. Note
Sometimes it is actually easier to work with surds!
Do not be in a rush to evaluate π