Question

what is the area of this triangle? 15? 9 select the best answer

Explanation:

Step1: Find the height of the triangle

This is a right - triangle. We can use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c = 15\) (hypotenuse) and \(b = 9\) (one of the legs). Let the height be \(a\). Then \(a=\sqrt{c^{2}-b^{2}}=\sqrt{15^{2}-9^{2}}=\sqrt{225 - 81}=\sqrt{144} = 12\).

Step2: Calculate the area of the triangle

The formula for the area of a triangle is \(A=\frac{1}{2}\times base\times height\). Here, the base \(b = 9\) and the height \(h=12\). So \(A=\frac{1}{2}\times9\times12\).
First, calculate \(9\times12 = 108\), then \(\frac{1}{2}\times108 = 54\).

Answer:

The area of the triangle is 54.