Your school is creating a community garden and painting a mural on the gym wall. You are the lead planner — use area formulas to size every plot and panel, then figure out the budget.
The school council gave you a $600 project budget and a blank wall plus four garden plots. Move through four phases: calculate the trapezoid garden plot, figure out paint for the triangular mural panel, measure the parallelogram banner, and make a budget decision about which plot fits the plan. Fill every calculator, hit Calculate or Check, then write your planning brief and print it.
The school garden has a trapezoid-shaped plot with two parallel sides (bases) and a perpendicular height. Use the trapezoid formula to find its area.
Add the two bases first, then multiply by the height, then divide by 2 (or multiply by ½). Example: b1 = 4, b2 = 6, h = 3 → ½ × (4 + 6) × 3 = ½ × 10 × 3 = 15 sq ft. The ½ accounts for the fact that a trapezoid is half of a parallelogram made from two copies.
One section of the gym mural is a large triangle. Find its area, then figure out how many cans of paint you need. Each can covers a set number of square feet — and you always round up to the next whole can because you can't buy a fraction of a can.
Step 1: Area = ½ × b × h. Step 2: Cans = Area ÷ coverage per can. Step 3: Round UP to the nearest whole number — even if you need 2.1 cans, you must buy 3. We use ceiling rounding (Math.ceil) because you cannot buy a partial can at the store.
The school banner hanging in the gym is a parallelogram. The fabric cost is priced by the square foot, so you need the exact area.
Use b × h — but make sure you use the perpendicular height, not the slant side. Example: b = 9, h = 4 → Area = 9 × 4 = 36 sq ft.
You are comparing two possible garden plots. Each has a cost per square foot. Find the total cost for each and decide which fits the $600 project budget for all materials combined.
Write a 3–5 sentence planning brief for the school council. Use your real numbers to explain the size of each space, how much paint is needed, and which garden plot you recommend.
| Category | 4 — Expert | 3 — Proficient | 2 — Developing |
|---|---|---|---|
| Trapezoid Area | Correct area using ½ × (b1 + b2) × h with formula clearly shown | Area is correct | Forgot the ½ or switched bases and height |
| Triangle Area | Correct area and paint cans correctly rounded up with explanation | Area and cans correct | Area correct but rounding error on cans |
| Parallelogram Area | Correct area using perpendicular height, not slant side | Area is correct | Used slant side or arithmetic error |
| Application / Communication | Budget decision correct; planning brief justifies recommendation with all numbers | Budget decision correct; brief uses most numbers | Decision unclear or missing numbers in brief |