Question

Find the area.
A = [?]cm²
4 cm, 3 cm and 5 cm
Shape: Triangle
Area of a triangle: A = bh/2

Answer 1

To find the area of a triangle when you have the lengths of all three sides, you can use Heron's formula. First, let's summarize the given side lengths:

- \( a = 4 \) cm
- \( b = 3 \) cm
- \( c = 5 \) cm

### Step 1: Calculate the semi-perimeter

The semi-perimeter \( s \) of the triangle is given by:

\[
s = \frac{a + b + c}{2} = \frac{4 + 3 + 5}{2} = \frac{12}{2} = 6 \, \text{cm}
\]

### Step 2: Apply Heron's formula

Heron's formula for the area \( A \) of a triangle is:

\[
A = \sqrt{s(s-a)(s-b)(s-c)}
\]

Substituting the values we have:

\[
A = \sqrt{6(6-4)(6-3)(6-5)}
\]

Calculating each term inside the square root:

- \( s - a = 6 - 4 = 2 \)
- \( s - b = 6 - 3 = 3 \)
- \( s - c = 6 - 5 = 1 \)

Now substitute these values into the formula:

\[
A = \sqrt{6 \times 2 \times 3 \times 1}
\]

### Step 3: Calculate the area

Now calculate the product under the square root:

\[
6 \times 2 = 12
\]
\[
12 \times 3 = 36
\]
\[
36 \times 1 = 36
\]

So, the area is:

\[
A = \sqrt{36} = 6 \, \text{cm}^2
\]

### Conclusion

The area of the triangle is:

\[
A = 6 \, \text{cm}^2
\]