Question

What is the number of parallelogram in figure?

• A. $27$
• B. $33$
• C. $34$
• D. $42$

Answer 1

The correct option is D $42$

There are 3 trips parallel to AB and 3 strips parallel to AC. There are 6 horizontal parallelograms in the first. 3 in the second and 1 in the third strip parallel to AB. Kite shaped parallelograms in these strips are $6+3+1=10$.
The pattern is repeated for strips parallel to AC except that topmost kite is common to both type of strips. There are 3 parallelograms each made up of 4 small parallelograms (horizontal and kite shaped.)
Hence total no. of parallelograms $=\left[2\right(10+10)-1]+3=42$.