Area by Heron's formula:
semiperimeter = (15 + 20 + 25)/2 = 60/2 = 30 cm
[tex]
Area = \sqrt{30(30-15)(30-20)(30-25)}= \sqrt{30 \cdot5\cdot10\cdot15}= \\\\ {} \ \ \ \ \ \ =\sqrt{22500} =150 \ cm^2[/tex]
The formula of the area of a triangle: Area = 1/2 * base * height
1/2 * 25 * height = 150
12.5 * height = 150
height = 150/12.5
height = 12 cm
