Question

1. what are the perimeter and area of rectangle abcd?
2. mike used a coordinate plane to design the patio shown at the right. each unit on the grid represents 1 yard. to buy materials to build the patio, mike needs to know its perimeter. what is the perimeter of the patio?

Explanation:

Step1: <Find the length and width of rectangle ABCD>

From the graph, the length of \(AB\) (or \(CD\)): The \(x\) - coordinate of \(A\) is \(- 4\) and of \(B\) is \(4\). Using the distance formula for horizontal distance \(d=\vert x_2 - x_1\vert\), \(AB=\vert4-(-4)\vert = 8\) units. The length of \(AD\) (or \(BC\)): The \(y\) - coordinate of \(A\) is \(-8\) and of \(D\) is \(8\). Using the distance formula for vertical distance \(d = \vert y_2 - y_1\vert\), \(AD=\vert8-(-8)\vert=16\) units.

Step2: <Calculate the perimeter of rectangle ABCD>

The formula for the perimeter of a rectangle is \(P = 2(l + w)\). Substitute \(l = 16\) and \(w = 8\) into the formula: \(P=2(16 + 8)=2\times24 = 48\) units.

Step3: <Calculate the area of rectangle ABCD>

The formula for the area of a rectangle is \(A=l\times w\). Substitute \(l = 16\) and \(w = 8\) into the formula: \(A=16\times8=128\) square units.

Answer:

The perimeter of rectangle \(ABCD\) is \(48\) units and the area is \(128\) square units.