Question

rectangle tera has vertices at t(5,6), e(7,4), r(-1,-4), and a(-3,-2).
find the area of rectangle tera.
round your answer to the nearest whole number.
use the keypad to enter the answer in the box provided.
the area of rectangle tera is square units.

Explanation:

Step1: Calculate the length of side \(TE\)

Use the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
For \(T(5,6)\) and \(E(7,4)\), \(x_1 = 5,y_1 = 6,x_2 = 7,y_2 = 4\).
\(TE=\sqrt{(7 - 5)^2+(4 - 6)^2}=\sqrt{4 + 4}=\sqrt{8}=2\sqrt{2}\)

Step2: Calculate the length of side \(ER\)

For \(E(7,4)\) and \(R(-1,-4)\), \(x_1 = 7,y_1 = 4,x_2=-1,y_2 = -4\).
\(ER=\sqrt{(-1 - 7)^2+(-4 - 4)^2}=\sqrt{64 + 64}=\sqrt{128}=8\sqrt{2}\)

Step3: Calculate the area of the rectangle

The area of a rectangle \(A = l\times w\). Here \(l = ER\) and \(w = TE\).
\(A=(2\sqrt{2})\times(8\sqrt{2})=2\times8\times2 = 32\)

Answer:

\(32\)