The diagram below shows how squares and lines could be arranged to form patterns of hexagons in a ro

Question

The diagram below shows how squares and lines could be arranged to form patterns of hexagons in a row.

The table below shows the number of squares and lines needed for Diagram $1$ to Diagram $4$.

Diagram ${n}$	${1}$	${2}$	${3}$	${4}$	$\ldots$
No. of squares	${6}$	${10}$	${14}$	${g}$	$\ldots$
No. of lines	${6}$	${11}$	${16}$	${h}$	$\ldots$

Find the value of ${g}$ and ${h}$.
Find the number of squares needed in Figure ${10}$.
Write down an expression, in terms of ${n}$, for
1. the number of squares needed for Diagram ${n}$,
2. the number of lines needed for Diagram ${n}$.

Accepted Answer

(a) $g = 18$, $h = 21$ (b) $42$ (c)(i) $4n + 2$ (ii) $5n + 1$

Diagram \({n}\)	\({1}\)	\({2}\)	\({3}\)	\({4}\)	\(\ldots\)
No. of squares	\({6}\)	\({10}\)	\({14}\)	\({g}\)	\(\ldots\)
No. of lines	\({6}\)	\({11}\)	\({16}\)	\({h}\)	\(\ldots\)

Hexagon Pattern: Number of Squares and Lines