Question

select all the expressions that can be used to find the area of the polygon.

18 ft
9 ft
6 ft
20 ft
(9 × 20) − 6
(9 × 18) − (6 × 2)
(9 × 18) + (6 × 2)
(20 × 6) + (18 × 3)
(20 × 9) − (3 × 2)

Explanation:

Step1: Calculate total area of big rectangle

$\text{Area}_\text{big} = 20 \times 9 = 180$ sq ft

Step2: Calculate missing small rectangle dimensions

Missing width: $20 - 18 = 2$ ft; Missing height: $9 - 6 = 3$ ft
$\text{Area}_\text{missing} = 2 \times 3 = 6$ sq ft

Step3: Verify expression 1: $(9×20)-6$

$180 - 6 = 174$ sq ft (matches polygon area)

Step4: Verify expression 2: $(9×18)-(6×2)$

$162 - 12 = 150$ sq ft (does not match)

Step5: Verify expression 3: $(9×18)+(6×2)$

$162 + 12 = 174$ sq ft (matches polygon area)

Step6: Verify expression 4: $(20×6)+(18×3)$

$120 + 54 = 174$ sq ft (matches polygon area)

Step7: Verify expression 5: $(20×9)-(3×2)$

$180 - 6 = 174$ sq ft (matches polygon area)

Answer:

• $(9 \times 20) - 6$
• $(9 \times 18) + (6 \times 2)$
• $(20 \times 6) + (18 \times 3)$
• $(20 \times 9) - (3 \times 2)$