Question

what is the area of triangle abc? round to the nearest hundredth of a square unit
17.75 square units
81.33 square units
372.71 square units
957.74 square units
herons formula: area = √s(s - a)(s - b)(s - c)

Explanation:

Step1: Calculate semi - perimeter

Let \(a = 12\), \(b = 14\), \(c = 16\). The semi - perimeter \(s=\frac{a + b + c}{2}=\frac{12+14 + 16}{2}=\frac{42}{2}=21\).

Step2: Apply Heron's formula

The area \(A=\sqrt{s(s - a)(s - b)(s - c)}=\sqrt{21(21 - 12)(21 - 14)(21 - 16)}=\sqrt{21\times9\times7\times5}=\sqrt{6615}\approx81.33\).

Answer:

81.33 square units