Answer:
(c) 39 mm²
Explanation:
You want to know an estimate of the area of the irregular figure.
Decomposition
The areas of irregular figures are often easily computed by decomposing the figure into shapes whose areas have formulas. Here, we can draw a vertical line from the upper left vertex to divide the figure into a triangle on the left and a trapezoid on the right.
Triangle
The triangle has a base of 3 squares and a height of 6 squares, so an area of ...
A = 1/2bh = 1/2(3)(6) = 9 . . . . square mm
Trapezoid
The trapezoid has vertical parallel bases of 6 and 7 squares, and a width of 5 squares. Its area is ...
A = 1/2(b1 +b2)h = 1/2(6 +7)(5) = 65/2 = 32 1/2 . . . . square mm
Total area
Then the total area of the figure shown is ...
area = triangle area + trapezoid area
area = 9 mm² +32.5 mm² = 41.5 mm²
The closest estimate of those offered is 39 square mm.