Answer:
Explanation:
We know that the area of the plane shape is given by A = (10x - 2) cm^2, and we also know that:
A is not greater than or equal to 12 cm^2 (i.e., A < 12), and
A is not less than 2 cm^2 (i.e., A > 2).
To find the smallest possible area of the shape, we need to find the smallest possible value of x that satisfies these conditions.
From the given conditions, we have:
10x - 2 < 12
10x < 14
x < 1.4
and
10x - 2 > 2
10x > 4
x > 0.4
Therefore, the smallest possible value of x that satisfies both conditions is:
0.4 < x < 1.4
To find the smallest possible area, we can substitute the lower bound of x into the area formula:
A = (10x - 2) cm^2
A = (10 × 0.4 - 2) cm^2
A = 2 cm^2
Therefore, the smallest possible area of the shape is 2 cm^2.