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Let's solve this problem step by step:

### (a) **Find the perimeter of the cross-section of the cutter**

The cross-section is a sector of a circle with center \( A \) and radius \( AB = AC = 6 \, \text{cm} \), along with a straight line segment for \( BC \).

The perimeter consists of:
- The two straight sides \( AB \) and \( AC \), each 6 cm.
- The arc length \( BC \), which can be calculated using the formula for the arc length of a sector:

\[
\text{Arc Length of } BC = r \theta
\]

Where:
- \( r = 6 \, \text{cm} \) (radius),
- \( \theta = 1.2 \, \text{radians} \) (angle in radians).

#### Step 1: Calculate the arc length

\[
\text{Arc Length of } BC = 6 \times 1.2 = 7.2 \, \text{cm}
\]

#### Step 2: Calculate the perimeter

The total perimeter \( P \) is the sum of the two straight sides \( AB \) and \( AC \), plus the arc length \( BC \):

\[
P = AB + AC + \text{Arc Length of } BC = 6 + 6 + 7.2 = 19.2 \, \text{cm}
\]

So, the perimeter is **19.2 cm**.

---

### (b) **Find the area of the cross-section \( ABC \)**

The area of the cross-section is the area of the sector formed by \( \triangle ABC \), which can be calculated using the formula for the area of a sector:

\[
\text{Area of sector } ABC = \frac{1}{2} r^2 \theta
\]

Where:
- \( r = 6 \, \text{cm} \) (radius),
- \( \theta = 1.2 \, \text{radians} \) (angle in radians).

#### Step 1: Calculate the area of the sector

\[
\text{Area of sector } ABC = \frac{1}{2} \times 6^2 \times 1.2 = \frac{1}{2} \times 36 \times 1.2 = 21.6 \, \text{cm}^2
\]

So, the area of the cross-section \( ABC \) is **21.6 cm²**.

---

### Final Answers:
- (a) The perimeter is **19.2 cm**.
- (b) The area is **21.6 cm²**.

Would you like more details or further explanations?

Here are 5 questions to deepen your understanding:
1. How does the formula for the arc length change if the angle is in degrees instead of radians?
2. Can you explain why the perimeter includes both the straight sides and the curved arc?
3. What happens to the perimeter and area if the angle \( \theta \) is doubled?
4. How would you compute the area if \( BC \) was a straight line instead of an arc?
5. How does the radius \( r \) affect both the perimeter and area formulas?

**Tip:** Always ensure that angles are in radians when using arc length and sector area formulas.

Find the perimeter and area of the cross-section ABC of a metal cutter used for making biscuits. The straight sides AB and AC are both 6 cm, and angle BAC is 1.2 radians. BC is an arc of a circle with centre A.

Calculate the perimeter and area of the cross-section ABC of a metal cutter. Learn how to use the arc length formula and sector area formula to solve this geometry problem involving radians. The sides are 6 cm, and the angle BAC is 1.2 radians.

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