In the figure, ABCD is a square, and all the dots are evenly spaced. Each vertical or horizontal distance between two adjacent dots is 3 units. Find the area of the shaded region.

A. 60

B. 72

C. 81

D. 96

E. 120

By close observation all the shaded region fits inside half of the squire.

As each dot to dot is 3 units, each side of the squire is 3*4=12 units.

The area of squire is 12^2=144

The area of the shaded region is 144/2 = 72

Answer. B

There are total 4*4 or 16 smaller squares of 3 units..
when we half them, it becomes 16*2=32 right angled triangles..
Now count the number of triangles that are shaded..
1st row - 3, 2nd row-5, 3rd row-5, and 4th row - 3, so total = 3+5+5+3=16..
so 16 out of 32 are shaded that is half of total ..
area = half of 12*12=72

Just found the diagram, I believe that is self explanatory.

Great! That's what I tried to tell in my previous post. Thank you for the diagram and detail explanation.

If the vertical or horizontal distance between two adjacent dots is 3 units, then the square has dimensions 12 by 12
So, the area of the ENTIRE SQUARE = (12)(12) = 144

Now, notice that the square is comprised of 32 identical triangles

Since 16 of the triangles are shaded, the shaded regions represent 16/32 (aka 1/2) of the ENTIRE SQUARE

In other words, the area of the shaded region = 1/2 of 144
= 72

Answer: B

Cheers,
Brent

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