Question

find the area of the polygon wxyz with its vertices at w(-3, -2), x(-3, 5), y(2, 5), and z(2, -2).
a) 70 square units
b) 35 square units
c) 12 square units
d) 24 square units

Explanation:

Step1: Determine the shape and side lengths

Plotting the points \(W(-3,-2)\), \(X(-3,5)\), \(Y(2,5)\), \(Z(2,-2)\) shows that \(WXYZ\) is a rectangle.
The length of \(WX\) (vertical side): \(|5 - (-2)|=|5 + 2| = 7\) (using the distance formula for points with the same \(x\) - coordinate \(d=\vert y_2 - y_1\vert\)).
The length of \(XY\) (horizontal side): \(|2-(-3)|=|2 + 3|=5\) (using the distance formula for points with the same \(y\) - coordinate \(d=\vert x_2 - x_1\vert\)).

Step2: Calculate the area of the rectangle

The area formula for a rectangle is \(A = \text{length}\times\text{width}\).
Substitute length \(l = 7\) and width \(w = 5\) into the formula: \(A=7\times5\).
\(A = 35\).

Answer:

B. 35 square units