Sodding a Yard Versus a Landscaper's Bid
A homeowner is replacing the lawn on a rectangular lot measuring 90 feet by 140 feet. The lot contains a rectangular house footprint of 42 feet by 55 feet, a detached garage measuring 22 feet by 24 feet, a circular patio 24 feet in diameter, and a rectangular driveway 20 feet by 40 feet. Grass will be installed everywhere else. Sod is sold only in full pallets, each covering 500 square feet, at $185 per pallet plus a flat $260 delivery fee. The supplier recommends ordering 8% extra to allow for cutting and overlaps, and charges 6.5% sales tax on the pallets but not on the delivery fee. A landscaper has bid $4,100 to supply and install the same sod, with all taxes and delivery included. The homeowner wants to know whether doing the work herself actually saves money, and she plans to use 3.14 for pi.
1. Determine the area that will be sodded, showing each subtraction.
Read the worked answer
Compute each region separately, then subtract the non-grass areas from the lot.
- Lot: 90 × 140 = 12,600 sq ft
- House: 42 × 55 = 2,310 sq ft
- Garage: 22 × 24 = 528 sq ft
- Patio: radius = 12 ft → 3.14 × 12² = 3.14 × 144 = 452.16 sq ft
- Driveway: 20 × 40 = 800 sq ft
Grass = 12,600 − 2,310 − 528 − 452.16 − 800 = 8,509.84 sq ft, about 8,510 sq ft.
Subtracting the areas rather than estimating is what makes the pallet count reliable; a 200 sq ft error here can be the difference between 18 and 19 pallets.
2. How many pallets must she buy, and what is the total cost including tax and delivery?
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Apply the 8% waste allowance first, then round up to whole pallets.
- Area with allowance: 8,509.84 × 1.08 = 9,190.63 sq ft
- Pallets: 9,190.63 ÷ 500 = 18.38 → 19 pallets (you cannot buy a fraction of a pallet, so always round up)
- Pallets: 19 × $185 = $3,515.00
- Sales tax on pallets only: $3,515 × 0.065 = $228.48
- Delivery (untaxed): $260.00
Total = $3,515.00 + $228.48 + $260.00 = $4,003.48.
3. Compare the do-it-yourself cost with the $4,100 bid, and evaluate the homeowner's idea of skipping the 8% waste allowance to save a pallet.
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DIY costs $4,003.48 versus $4,100, a saving of $96.52, roughly 2.4%. That margin is thin: one additional pallet with tax costs about $197, which would put DIY above the bid.
Skipping the 8% allowance: 8,509.84 ÷ 500 = 17.02 → 18 pallets. Cost = 18 × $185 = $3,330, tax $216.45, plus $260 delivery = $3,806.45, saving $293.55. But 18 pallets supply 9,000 sq ft against 8,509.84 needed - only 490 sq ft, or 5.8%, of slack, below the supplier's own recommendation. Diagonal cuts around the circular patio and at corners typically waste more than that, and running short means a second delivery plus a second trip.
The sensible judgment: keep the 8% allowance, expect a saving near $100 rather than $300, and recognize the real risk is that the saving is small enough that an error or a second delivery erases it. Using 3 instead of 3.14 for pi changes the patio to 432 sq ft, a 20 sq ft difference that does not change the pallet count at all.