Question

find the lateral area of the triangular prism. 16 m 12 m 20 m square meters

Explanation:

Step1: Identify side lengths of base triangle

The base - triangle has sides of lengths \(12m\), \(16m\), and we can find the hypotenuse using the Pythagorean theorem \(c=\sqrt{a^{2}+b^{2}}\), where \(a = 12m\) and \(b = 16m\). So \(c=\sqrt{12^{2}+16^{2}}=\sqrt{144 + 256}=\sqrt{400}=20m\).

Step2: Recall formula for lateral area of triangular prism

The lateral area \(L\) of a triangular prism is \(L=(a + b + c)h\), where \(a\), \(b\), \(c\) are the side - lengths of the base triangle and \(h\) is the height of the prism. Here \(a = 12m\), \(b = 16m\), \(c = 20m\) and \(h=26m\).

Step3: Calculate lateral area

\(L=(12 + 16+20)\times26=(48)\times26 = 1248m^{2}\).

Answer:

1248