To calculate the area of a triangle using the formula \( A = \frac{bh}{2} \), we typically need the base \( b \) and the height \( h \). However, in your case, it sounds like you are dealing with a triangle where you have the lengths of all three sides: 12 cm, 10 cm, and 15 cm.
When you don't have the height, you can use Heron's formula to calculate the area of the triangle. Heron's formula is given by:
\[ A = \sqrt{s(s-a)(s-b)(s-c)} \]
where \( s \) is the semi-perimeter, and \( a, b, c \) are the lengths of the sides of the triangle.
- First, calculate the semi-perimeter \( s \):
\[ s = \frac{a + b + c}{2} = \frac{12 + 10 + 15}{2} = \frac{37}{2} = 18.5 \text{ cm} \]
- Now we apply the values into Heron's formula:
\[ A = \sqrt{s(s-a)(s-b)(s-c)} \] \[ A = \sqrt{18.5(18.5 - 12)(18.5 - 10)(18.5 - 15)} \] \[ A = \sqrt{18.5(6.5)(8.5)(3.5)} \]
- Now, calculate the values step-by-step:
\[ 18.5 - 12 = 6.5 \] \[ 18.5 - 10 = 8.5 \] \[ 18.5 - 15 = 3.5 \]
- Multiply the terms inside the square root:
\[ A = \sqrt{18.5 \times 6.5 \times 8.5 \times 3.5} \]
Calculating this step-by-step:
- First multiply \( 6.5 \times 8.5 = 55.25 \)
- Then multiply \( 55.25 \times 3.5 = 193.375 \)
- Finally multiply \( 193.375 \times 18.5 = 3578.4375 \)
Now take the square root:
\[ A = \sqrt{3578.4375} \approx 59.8 \text{ cm}^2 \]
Thus, the area of the triangle is approximately:
\[ A \approx 59.8 , \text{cm}^2 \]