To find the area of a triangle, we can use the formula \( A = \frac{1}{2} \times b \times h \), where \( b \) is the base and \( h \) is the height.
In your case, you provided three side lengths (8 cm, 4 cm, and 7 cm), but we need to determine which one to use as the base and height. Since only two of the three sides are necessary to use in the area formula, we'll need to first use Heron's formula to find the area, as there is no clear indication of which sides are base and height.
- First, let's find the semi-perimeter \( s \) of the triangle:
\[ s = \frac{a + b + c}{2} = \frac{8 + 4 + 7}{2} = \frac{19}{2} = 9.5 \text{ cm} \]
- Now, we can use Heron's formula to find the area \( A \):
\[ A = \sqrt{s(s-a)(s-b)(s-c)} \]
where \( a = 8 \text{ cm}, b = 4 \text{ cm}, c = 7 \text{ cm} \).
- Substitute the values:
\[ A = \sqrt{9.5 \times (9.5 - 8) \times (9.5 - 4) \times (9.5 - 7)} \] \[ A = \sqrt{9.5 \times 1.5 \times 5.5 \times 2.5} \]
- Calculate the individual components:
\[ 9.5 - 8 = 1.5 \] \[ 9.5 - 4 = 5.5 \] \[ 9.5 - 7 = 2.5 \]
- Putting it all together:
\[ A = \sqrt{9.5 \times 1.5 \times 5.5 \times 2.5} \] \[ = \sqrt{9.5 \times 1.5 \times 5.5 \times 2.5} \approx \sqrt{9.5 \cdot 1.5 \cdot 5.5 \cdot 2.5} \approx \sqrt{9.5 \cdot 20.625} \approx \sqrt{195.9375} \approx 14.0 \text{ cm}^2 \]
Therefore, the area \( A \) of the triangle is approximately:
\[ A \approx 14.0 \text{ cm}^2 \]
So the area is:
\[ A = 14 \text{ cm}^2 \]
Final answer: \( A = 14 \text{ cm}^2 \)