You are the lead architect for Bayside Parks. The city wants a riverfront park built around a triangular shade pavilion. Use scale drawings and area math to plan every surface, choose materials, estimate the cost, and bring the build in under $60,000.
The city handed you a scaled site plan. Every blueprint on this page uses the same scale:
SCALE 1 grid square = 1 meter · site plan drawn to scale
Area is how much flat surface a shape covers, measured in square meters (m²). For a tricky shape, cut it into rectangles and triangles you know, find each area, then add them up.
Español: El área es la superficie plana que cubre una figura, medida en metros cuadrados (m²). Para una figura difícil, córtala en rectángulos y triángulos, halla cada área y súmalas.Composite strategy — Decompose (cut the shape into pieces) or Compose (frame a big rectangle, then subtract the missing corner). Both give the same area; pick the one with fewer steps.
The signature pavilion has a triangular fabric roof. Read its dimensions off the scale blueprint, then size and price the shade fabric.
Q1.1 — Area of the triangular roof
Q1.2 — Shade fabric costs $22 / m². What is the fabric cost?
Triangle area = ½ × base × height. Multiply the two numbers, then take half. Cost = area × price per m².
Español: Área del triángulo = ½ × base × altura. Costo = área × precio por m².The paved entry plaza is an L-shape. Decompose it into two rectangles, find each area, then add. The colored regions on the blueprint show the cuts.
Q2.1 — Area of Region A (upper-left, 8 m × 6 m)
Q2.2 — Area of Region B (bottom strip, 16 m × 6 m)
Q2.3 — Total plaza area (A + B)
An L-shape splits cleanly into two rectangles. Area of a rectangle = length × width. Add the two rectangle areas for the total.
Español: Una forma de L se divide en dos rectángulos. Área = largo × ancho. Suma las dos áreas para el total.Prove it two ways. Decompose: region A + region B. Now compose: frame the whole 16 × 12 rectangle and subtract the missing corner. Do you get the same answer? Which method used fewer steps here, and why?
The garden follows the curve of the river, so it is shaped like a trapezoid. Find its area, choose a ground cover, and watch the live cost update.
Q3.1 — Area of the trapezoidal garden
Live cost = 135 m² × price/m². This feeds straight into your Budget Board in Task 4.
Bring it together. Enter the roof and plaza costs you computed; the garden cost auto-fills from your material choice. Then tally the build against the $60,000 budget.
| Surface | Area (m²) | Your cost ($) |
|---|---|---|
| Pavilion roof — fabric @ $22/m² | 108 | |
| Entry plaza — paving @ $35/m² | 144 | |
| Riverbank garden — your material | 135 | |
| Site labor — fixed | — | |
| Total estimate | $0 |
Plaza paving cost = 144 m² × $35. Compute it and enter it to confirm you can turn area into money.
Total = roof + plaza + garden + labor. Remaining = budget − total. Positive remaining = under budget (good). Negative = pick a cheaper material.
Español: Total = techo + plaza + jardín + mano de obra. Restante = presupuesto − total. Si el restante es positivo, estás dentro del presupuesto.If river-stone ($20/m²) pushes you over budget, what is the highest garden material price p you can still afford? Using your computed roof cost, plaza cost, garden area, and the $38,000 labor, write and solve:
labor + roof cost + plaza cost + 135·p ≤ 60,000
When every surface checks out and your plan is under budget, submit it to the city council. Enter your name in the field below, then press Submit plan & grade to save your score as a PDF or DOC.
| Level | Score | Descriptor |
|---|---|---|
| 4 — Exceeds | 6 / 6 | Reads every scale drawing accurately and applies triangle, composite, and trapezoid area formulas correctly. Brings the build under budget and can explain the decompose/compose strategies and the budget inequality. |
| 3 — Meets | 5 / 6 | Correctly computes most surface areas and costs with at most one arithmetic slip. Completes the budget board and reaches a valid under-budget plan. |
| 2 — Approaching | 3–4 / 6 | Computes simple areas but struggles with the composite figure or trapezoid (e.g., forgets to halve, or does not add both bases). Partial cost/budget work. |
| 1 — Beginning | 0–2 / 6 | Few correct areas. Confuses formulas or misreads the scale. Needs reteaching on area formulas and reading scale drawings. |