find the area of the triangle below. carry your intermediate computations to at least four decimal places…

Explanation:

Step1: Calculate semi - perimeter

Let (a = 8), (b = 11), (c=15.4). The semi - perimeter (s=\frac{a + b + c}{2}=\frac{8 + 11+15.4}{2}=\frac{34.4}{2}=17.2).

Step2: Use Heron's formula

The area (A=\sqrt{s(s - a)(s - b)(s - c)}=\sqrt{17.2(17.2 - 8)(17.2 - 11)(17.2 - 15.4)}=\sqrt{17.2\times9.2\times6.2\times1.8}). First, calculate (17.2\times9.2\times6.2\times1.8 = 17.2\times(9.2\times6.2\times1.8)=17.2\times(57.04\times1.8)=17.2\times102.672 = 1766.9584). Then, (A=\sqrt{1766.9584}\approx42.0352).

Step3: Round the answer

Rounding (42.0352) to the nearest tenth gives (42.0).

Answer:

(42.0) m²