Question

fill - in - the - blank text item interaction
find the area of polygon stuv below. each unit on the graph measures 1 centimeter. round
your answer to the nearest tenth, if necessary.
the area of polygon stuv is \\( \mathrm{cm}^{2} \\).

Explanation:

Step1: Find the lengths of the diagonals

The diagonals of the rhombus \(STUV\) can be found using the distance formula (or by counting units on the coordinate - grid).
The vertical diagonal \(s\): The \(y\) - coordinates of \(S(2,6)\) and \(U(2, - 1)\). The length \(s=\vert6-( - 1)\vert=7\) cm.
The horizontal diagonal \(t\): The \(x\) - coordinates of \(V(-2,2)\) and \(T(5,2)\). The length \(t=\vert5-( - 2)\vert = 7\) cm.

Step2: Use the formula for the area of a rhombus

The formula for the area of a rhombus is \(A=\frac{1}{2}s\times t\), where \(s\) and \(t\) are the lengths of the diagonals.
Substitute \(s = 7\) and \(t = 7\) into the formula: \(A=\frac{1}{2}\times7\times7\).

$$A=\frac{49}{2}=24.5$$

Answer:

\(24.5\)