Question

1. two hexagons are shown in the coordinate plane.

a. are the hexagons congruent?
b. find the area of each hexagon.

Explanation:

Step1: Determine congruence

Congruent figures have the same shape and size. By visual inspection (or counting unit - squares for side - lengths), the two hexagons have the same shape and size.

Step2: Calculate area (using the formula for the area of a composite shape by counting unit - squares)

Count the number of unit - squares in each hexagon. Each unit - square has an area of \(1\) square unit.
For the first hexagon:
Count the rows and columns of unit - squares. We can break it into two rectangles. One rectangle has dimensions \(3\times5\) (area \(A_1 = 3\times5=15\)) and another has dimensions \(2\times2\) (area \(A_2=2\times2 = 4\)). The total area \(A=15 + 4=19\) square units.
For the second hexagon:
Similarly, break it into two rectangles. One rectangle has dimensions \(3\times5\) (area \(A_1 = 3\times5 = 15\)) and another has dimensions \(2\times2\) (area \(A_2=2\times2=4\)). The total area \(A = 15+4=19\) square units.

Answer:

a. Yes, the hexagons are congruent.
b. The area of each hexagon is \(19\) square units.