Question

How many squares are there in the given figure?

• A. \(32\)
• B. \(48\)
• C. \(78\)
• D. \(70\)

Hint:

In grid problems, never stop at counting unit squares—always look for larger squares formed by combining them.

Answer 1

The Correct Option is D

Concept: To count the total number of squares in a rectangular grid, we must count:
All the smallest unit squares,
All larger squares formed by combining smaller ones. If a grid has \(m\) rows and \(n\) columns, the total number of squares is: \[ \sum_{k=1}^{\min(m,n)} (m-k+1)(n-k+1) \]
Step 1: Identify the grid size From the figure: \[ \text{Number of rows } = 4,\quad \text{Number of columns } = 8 \]
Step 2: Count squares of different sizes
\(1 \times 1\) squares: \[ 4 \times 8 = 32 \]
\(2 \times 2\) squares: \[ 3 \times 7 = 21 \]
\(3 \times 3\) squares: \[ 2 \times 6 = 12 \]
\(4 \times 4\) squares: \[ 1 \times 5 = 5 \]
Step 3: Add all squares \[ 32 + 21 + 12 + 5 = 70 \]
Final Answer: \(\boxed{70}\)