Step by step
The question
Question: a sector has radius 4 cm and angle 135°: find the area of the sector.
A sector is a slice of the circle, like a slice of pizza.
1 What part of the circle
A whole turn is 360°.
The slice is 135° out of 360°: that is 3/8 of the circle.
part = 135°360° = 38
135 and 360 can both be divided by 45.
135 ÷ 45 = 3, 360 ÷ 45 = 8
2 Whole circle
The area of the whole circle is π r squared: π times 16 is 16π.
circle area = π × 4² = 16π
Careful!
Area uses r squared: 4 times 4.
Not 2 r.
Careful: not π × 4 × 2 = 8π ✗
3 Take the part
Now 3/8 of 16π: 6π.
sector area = 38 × 16π = 6π
In π that is 6π.
As a decimal: about 18.85 cm², to 2 decimal places.
≈ 6π ≈ 18.85 cm²
4 Check
Let's check: the whole is 8/3 times the part: 16π again.
So it is right!
83 × 6π = 16π
Let's look back.
First: what part of the circle.
Then: whole circle.
Then: take the part.
Last: check.
Answer
≈ 6π ≈ 18.85 cm²