Question

question 28 (5 points)
find the area of the polygon shown in the figure.
12 square units
16 square units
36 square units
12 + 4\sqrt{5} square units

Explanation:

Step1: Determine the base and height of the triangle

From the figure, for triangle \(PQR\), the base \(QR\) can be found by counting the units on the \(x -\)axis. The \(x -\)coordinate of \(Q\) is \(1\) and of \(R\) is \(5\), so \(QR=\vert5 - 1\vert=4\) units. The height is the vertical distance from \(P\) to \(QR\). The \(y -\)coordinate of \(P\) is \(5\) and of \(Q\) (or \(R\) in terms of vertical alignment for height) is \(-1\), so the height \(h=\vert5-(- 1)\vert = 6\) units.

Step2: Use the formula for the area of a triangle

The formula for the area of a triangle is \(A=\frac{1}{2}\times base\times height\). Substitute \(base = 4\) and \(height=6\) into the formula: \(A=\frac{1}{2}\times4\times6\).
First, calculate \(4\times6 = 24\), then \(\frac{1}{2}\times24=12\).

Answer:

12 square units