What is the area of triangle PQR is PQ is 5.5cm, QR is 2.65cm, and PR is 3.6cm?

To find the area of triangle PQR with the given side lengths, we can use **Heron's formula**. Heron's formula calculates the area of a triangle when all three side lengths are known.

### Steps:

1. **Find the semi-perimeter (s):**
   \[
   s = \frac{PQ + QR + PR}{2}
   \]

2. **Apply Heron's formula:**
   \[
   \text{Area} = \sqrt{s(s - PQ)(s - QR)(s - PR)}
   \]

Now, let's calculate the area step by step.

- \( PQ = 5.5 \) cm
- \( QR = 2.65 \) cm
- \( PR = 3.6 \) cm

### Step 1: Semi-perimeter (s)
\[
s = \frac{5.5 + 2.65 + 3.6}{2}
\]

### Step 2: Area calculation
\[
\text{Area} = \sqrt{s(s - 5.5)(s - 2.65)(s - 3.6)}
\]

I'll calculate this for you now.The area of triangle PQR is approximately \( 4.02 \, \text{cm}^2 \).

Would you like further details, or do you have any questions?

Here are 5 related questions to explore further:

1. How do you find the perimeter of triangle PQR with the given side lengths?
2. What is Heron’s formula, and why is it useful for calculating the area of a triangle?
3. How can the height of triangle PQR be found using the area and base?
4. What are the conditions for a triangle to exist based on the lengths of its sides?
5. How does Heron's formula compare to other methods for finding the area of a triangle?

**Tip:** Heron's formula is especially useful for non-right-angled triangles, where height isn't readily known.

Learn how to calculate the area of triangle PQR using Heron's formula with side lengths PQ = 5.5cm, QR = 2.65cm, and PR = 3.6cm. Follow a step-by-step solution to find the area of a triangle given all three sides. Suitable for Grades 7-9.

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