Question

plot and connect the points a(4, 1), b(1, 1), c(1, -6), d(4, -6), and find the area of figure abcd.
a. 27 square units
b. 12 square units
c. 21 square units
d. 18 square units

Explanation:

Step1: Determine the length of the sides

For side \(AB\): \(x\)-coordinates of \(A(4,1)\) and \(B(1,1)\). Length \(AB=\vert4 - 1\vert=3\) (since \(y\)-coordinates are the same).
For side \(BC\): \(y\)-coordinates of \(B(1,1)\) and \(C(1,-6)\). Length \(BC=\vert1-(-6)\vert = 7\) (since \(x\)-coordinates are the same).

Step2: Use the formula for the area of a rectangle

Since \(AB\) and \(BC\) are adjacent sides of a rectangle (right - angled, as \(AB\) is horizontal and \(BC\) is vertical), area \(A = AB\times BC\).
Substitute \(AB = 3\) and \(BC=7\) into the formula: \(A=3\times7 = 21\).

Answer:

C. 21 square units