Question

find the area of this triangle. 155 175 260 area = ? units² round to the nearest whole number.

Explanation:

Step1: Calculate semi - perimeter

Let \(a = 155\), \(b=175\), \(c = 260\). The semi - perimeter \(s=\frac{a + b + c}{2}=\frac{155+175 + 260}{2}=\frac{590}{2}=295\).

Step2: Apply Heron's formula

The area \(A=\sqrt{s(s - a)(s - b)(s - c)}\). Substitute the values: \(A=\sqrt{295(295 - 155)(295 - 175)(295 - 260)}=\sqrt{295\times140\times120\times35}\).
First, calculate \(295\times140\times120\times35=(300 - 5)\times140\times120\times35=(42000-700)\times120\times35 = 41300\times120\times35=4956000\times35 = 173460000\).
Then \(A=\sqrt{173460000}\approx13169\).

Answer:

13169