Can someone asap! find the area of the shaded region using pick's theorem. a. 35 b. 15 c. 20 d. 20.5

Pick’s Theorem is used to find the areas of figures on lattices easily. The formula is:

A = (B)/2 + I - 1, where B is the number of points on the border of the shape, and I is the number of points inside the shape.

Here, there are 8 points on the outside of the shape, and there are 12 points inside the shape. So, we do:

8/2 + 12 - 1 = 4 + 12 - 1 = 15 units squared.

We can check by finding the areas of the non-shaded region and subtracting that area from the whole rectangle area of 4 * 10 = 40:

4 * 1 + (3 * 1)/2 + 1 * 9 + (3 * 1)/2 + (9 * 2)/2 = 25

40 - 25 = 15, so we’re right!

The answer is 15 units squared, or choice (B).

g

step-by-step explanation: