Find the area of each of the figures drawn on the unit square grid paper given below:
(Note: Each unit square has side 1 cm.)
Answer
Full Squares: Counting the solid blue boxes in the main body and sleeves, we get approximately 48 full squares.
∴ 48 full squares = 48 cm2
Half or More Squares: The slanted parts of the sleeves and the curved neckline contribute about 12 squares that are half or more filled.
∴ 12 full squares = 12 cm2
Less than Half: We ignore the squares which are less than half.
Total Area: (48 + 12) cm2 = 60 cm2.
The area of T-shirt = 60 cm2.
Full Squares: Counting the complete, solid blue squares within the neck and the main body of the bottle:
Neck: 4 full squares
Main Body: 47 full squares
Total Full Squares = 51
Area of Full Squares = 51 cm2
Half or More Squares: These are the squares along the slanted "shoulders" and the rounded base corners that are at least half-filled.
Shoulder Slants: 3 squares
Rounded Base: 2 squares
Total Half or More Squares = 5
Area of these Squares = 5 cm2
Less than Half Squares: These are the tiny slivers at the very edges of the rounded corners and the shoulder joints.
Ignore these squares and count them as 0 cm2
Total Area = (51 + 5) cm2 = 56 cm2
The area of Bottle = 56 cm2.
Dividing the shape into rectangles A, B, and C:
Rectangle A (Top Bar): 8 wide x 2 high = 16 cm2
Rectangle B (Middle): 2 wide x 5 high = 10 cm2
Rectangle C (Bottom Bar): 10 wide x 2 high = 20 cm2
Total Area: (16 + 10 + 20) cm2 = 46 cm2
Total area = 46 cm2.
Dividing the shape into rectangles A, B, C and D:
Rectangle A (Backbone): 2 wide x 12 high = 24 cm2
Rectangle B (Top Arm): 6 wide x 2 high = 12 cm2
Rectangle C (Middle Arm): 4 wide x 2 high = 8 cm2
Rectangle D (Bottom Arm): 6 wide x 2 high = 12 cm2
Total Area: (24 + 12 + 8 + 12) cm2 = 56 cm2
Total area = 56 cm2.