Question

use the coordinates to compute the approximate area of the rectangle. (1 point) 40 units² 30 units² 10 units² 20 units²

Explanation:

Step1: Calculate the length of the base

The base can be calculated by finding the distance between \(x -\)coordinates of two points. Let's take \(A(-3,-1)\) and \(D(3,1)\). The horizontal distance (base \(b\)): \(b=\vert3 - (- 3)\vert=6\) (using the formula for the distance between two points \(x_1\) and \(x_2\) on the \(x -\)axis \(d=\vert x_2 - x_1\vert\)).

Step2: Calculate the height

The height can be calculated by finding the vertical distance. Let's consider the vertical spread. If we assume a rectangle - like structure (using the vertical distances from the figure's approximate shape). The height \(h\) (approximate vertical distance, for example, from \(y=-4\) to \(y = 1\)): \(h=\vert1-(-4)\vert = 5\) (using the formula for the distance between two points \(y_1\) and \(y_2\) on the \(y -\)axis \(d=\vert y_2 - y_1\vert\)).

Step3: Calculate the area of the rectangle

The area of a rectangle is given by the formula \(A=b\times h\). Substitute \(b = 6\) and \(h=5\) into the formula: \(A=6\times5 = 30\) (using the area formula \(A=b\times h\)).

Answer:

\(30\) units\(^{2}\)