Question

How many rectangles are in the following figure?

• A. 18
• B. 19
• C. 16
• D. 17

Answer 1

Answer: (A)

18

The rectangles that are easily spotted are $\left(ABML\right),\left(BCNM\right),\left(CDON\right),\left(NOEF\right)\left(MNGF\right)$ and $\left(LMGH\right)$.

These are $6$ in number.

Now let us count the rectangle made from two components. These are the rectangles $\left(ACNL\right),\left(BDOM\right),\left(LNFH\right),\left(MOEG\right)\left(ABGH\right),\left(BCGF\right)$ and $\left(LMGH\right)$.

These are $7$ in number.

Now, the number of rectangles that are made up of three components each. These are $\left(ALOD\right)$ and $\left(HLOE\right)$.

These are $2$ in number.

Now, the number of rectangles that are made up of four components each. These are $\left(ACFH\right)$ and $\left(BDEG\right)$.

These are $2$ in number.

and the rectangle made up of all the components, i.e., $\left(ADEH\right)$.

Therefore,

Total no. of rectangles $=6+7+2+2+1=18$

Hence there are $18$ rectangles.