Fencing and Sodding a Corner Lot
A homeowner has a rectangular backyard measuring 18 meters by 12 meters. She wants to fence the entire perimeter, leaving a 1-meter-wide gate gap with no fence. Fence panels come in 2-meter sections and can only be bought whole; each panel costs $35. Separately, she wants to sod the lawn but must leave a rectangular patio area of 4 m × 3 m unsodded, and a 0.5-meter-wide border along all four inside edges of the yard must stay bare (no sod) for drainage. Sod is sold in bags covering 5 square meters each, and only whole bags can be purchased.
1. How many fence panels must she buy, and what is the fence cost?
Read the worked answer
Perimeter = 2(18 + 12) = 2(30) = 60 m. Subtract gate gap: 60 − 1 = 59 m of fence needed. Panels are 2 m each: 59 ÷ 2 = 29.5 → must round up to 30 panels (can't buy half a panel). Cost = 30 × $35 = $1,050. Key judgment: rounding up, not to nearest. 29 panels = 58 m, which leaves a 1 m shortfall.
2. How many bags of sod are needed? Show the area accounting including the drainage border and patio.
Read the worked answer
Total yard area = 18 × 12 = 216 m². The 0.5 m border runs along all four inside edges. The sodable inner rectangle is reduced by 0.5 m on each side:
- width: 18 − 2(0.5) = 17 m
- length: 12 − 2(0.5) = 11 m Inner area = 17 × 11 = 187 m². Subtract patio: 187 − (4 × 3) = 187 − 12 = 175 m² to sod. Bags: 175 ÷ 5 = 35 exactly → 35 bags. Judgment: the border must be subtracted on both sides of each dimension (2 × 0.5), a common error is subtracting only 0.5 once per dimension.