Question

in the diagram below, \\( \overrightarrow { d r } \\) is perpendicular to \\( \overline { o p } \\).

find the area of \\( \triangle d u o \\).
if entering your answer as a decimal, round your final answer to the nearest
hundredth.

\\( \square \\) square units

Explanation:

Step1: Determine the base and height of the triangle

The base \(OD\) of \(\triangle DUO\) is \(4.0 + 10.0=14.0\) units. The height \(UM\) is equal to the length \(AP = 4.5\) units (since \(UM\) and \(AP\) are both perpendicular to \(OP\) and the figure likely has some parallel - like properties or is constructed in a way that these perpendiculars are equal).

Step2: Use the area formula for a triangle

The area formula for a triangle is \(A=\frac{1}{2}\times base\times height\). Substitute \(base = 14.0\) and \(height = 4.5\) into the formula:

$$A=\frac{1}{2}\times14.0\times4.5$$

$$A = 7\times4.5$$

$$A=31.5$$

Answer:

\(31.50\)