How many Squares? — Important Questions

60 square units

Step 1: A 10×6 rectangle has 10 columns and 6 rows. Step 2: Area = length × width = 10 × 6 = 60 square units. Step 3: We can verify: 12 pentomino shapes × 5 squares each = 60 square units total. Both methods give the same answer, confirming it is correct. The mistake of adding 10+6=16 confuses area with perimeter!

Both rectangles have the same area but may have different perimeters

Step 1: Two rectangles can have the same area but different shapes, e.g., 4×6 and 3×8 both have area 24. Step 2: Perimeter of 4×6 = 2×(4+6) = 20. Perimeter of 3×8 = 2×(3+8) = 22. Different perimeters! Step 3: So same area does NOT mean same perimeter. This is a key concept: area and perimeter are independent properties of shapes.

9 square cm

Step 1: The original square has side 3 cm. Area of square = 3 × 3 = 9 square cm. Step 2: When Ziri cuts a triangle from one side and adds it to another side, she is only rearranging pieces, NOT adding or removing any area. Step 3: The total area remains 9 square cm. This concept is called conservation of area — rearranging pieces does not change total area!

10 square cm

Step 1: A diagonal divides a rectangle into exactly two equal triangles. Step 2: Each triangle has area = Total rectangle area ÷ 2 = 20 ÷ 2. Step 3: Area of each triangle = 10 square cm. Verify: 10 + 10 = 20 ✓. Common error: Dividing by 4 instead of 2, giving 5. Remember, a diagonal makes 2 triangles, not 4!