what's the surface area of this triangle? the measurements are...
8mm
12mm
10mm
15mm
To calculate the surface area of a triangle, we can use Heron's formula:
s = (a + b + c) / 2
where s is the semiperimeter and a, b, and c are the side lengths of the triangle. In this case:
a = 8mm
b = 12mm
c = 10mm
s = (8 + 12 + 10) / 2
s = 30 / 2
s = 15
Now, we can calculate the surface area using Heron's formula:
Area = sqrt(s * (s - a) * (s - b) * (s - c))
Area = sqrt(15 * (15 - 8) * (15 - 12) * (15 - 10))
Area = sqrt(15 * 7 * 3 * 5)
Area = sqrt(1575)
Area ≈ 39.68 mm^2
Therefore, the surface area of the triangle is approximately 39.68 mm^2.