Question

the vertices of a rectangle are listed below. e(2, 3), f(2, 9), g(11, 9), h(11, 3) what is the area of the rectangle? a. 30 square units b. 108 square units c. 54 square units d. 216 square units

Explanation:

Step1: Calculate the length of the rectangle

The length can be found by calculating the horizontal distance between two points with the same \(y\) - coordinate. For points \(E(2,3)\) and \(H(11,3)\) (or \(F(2,9)\) and \(G(11,9)\)), using the distance formula \(d=\vert x_2 - x_1\vert\). Here, \(x_1 = 2,x_2=11\), so \(l=\vert11 - 2\vert=9\).

Step2: Calculate the width of the rectangle

The width can be found by calculating the vertical distance between two points with the same \(x\) - coordinate. For points \(E(2,3)\) and \(F(2,9)\) (or \(G(11,9)\) and \(H(11,3)\)), using the distance formula \(d=\vert y_2 - y_1\vert\). Here, \(y_1 = 3,y_2 = 9\), so \(w=\vert9 - 3\vert=6\).

Step3: Calculate the area of the rectangle

The area formula of a rectangle is \(A = l\times w\). Substitute \(l = 9\) and \(w = 6\) into the formula, we get \(A=9\times6 = 54\).

Answer:

C. 54 square units