Find the area (in sq. units) of the region bounded by the graph | x – 7 | + | y – 9 | = 12

The given equation |x – 7| + |y – 9| = 12 represents a rhombus with vertices at (7, 21), (7, -3), (-5, 9), and (19, 9) in the xy-plane.

The area of a rhombus is given by the formula: Area = 1/2 * d1 * d2, where d1 and d2 are the lengths of the diagonals.

The length of the diagonals of the rhombus can be found using the distance formula: d = sqrt[(x2 - x1)^2 + (y2 - y1)^2]

The length of the first diagonal (d1) is the distance between the points (7, 21) and (7, -3), which is: d1 = sqrt[(7 - 7)^2 + (21 - (-3))^2] = sqrt[0 + 24^2] = 24 units.

The length of the second diagonal (d2) is the distance between the points (-5, 9) and (19, 9), which is: d2 = sqrt[(19 - (-5))^2 + (9 - 9)^2] = sqrt[24^2 + 0] = 24 units.

Substituting d1 = 24 units and d2 = 24 units into the formula for the area of a rhombus, we get: Area = 1/2 * 24 * 24 = 288 square units.

So, the area of the region bounded by the graph |x – 7| + |y – 9| = 12 is 288 square units.