Question

what is the area of this triangle? 12 (dashed line with arrows, vertical), 13 (dashed line with arrows, slant), and a right triangle with a right angle marked by a red square, and a ? inside the triangle.

Explanation:

Step1: Find the base length

The triangle is right - angled (indicated by the right - angle symbol). We can use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c = 13\) (hypotenuse) and \(a = 12\) (one leg). Let the base be \(b\). Then \(b=\sqrt{c^{2}-a^{2}}=\sqrt{13^{2}-12^{2}}=\sqrt{169 - 144}=\sqrt{25} = 5\).

Step2: Calculate the area

The formula for the area of a right - angled triangle is \(A=\frac{1}{2}\times base\times height\). Here, the height \(h = 12\) and the base \(b = 5\). So \(A=\frac{1}{2}\times5\times12=30\).

Answer:

30