Determine the Area of Trapezoids Challenge

Grade 6 Math · Unit 5 Challenge Studio (6.GR.1) · Lesson 5-3
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I can find the area of a trapezoid using the formula A = ½(b1 + b2) × h.Puedo hallar el área de un trapecio usando la fórmula A = ½(b1 + b2) × h.

MissionMisión · Reef RescueRescate del arrecife · night shiftturno de noche

Protect the coral, one calculation at a time.Protege el coral, un cálculo a la vez.

Night dive: the reef glows, and the glow-in-the-dark markers on the nursery trays need shade cloth before the tide turns. Work out each area carefully, because the supply boat only comes once.

Inmersión nocturna: el arrecife brilla, y los marcadores fluorescentes de las bandejas del criadero necesitan tela de sombra antes de que cambie la marea. Calcula cada área con cuidado, porque el barco de suministros solo viene una vez.

Word bankBanco de palabras 4 words4 palabrastrapezoid, bases (b₁, b₂), height, …trapecio, bases (b₁, b₂), altura, …
trapezoidtrapecio
A four-sided shape with just one pair of parallel sides.Una figura de cuatro lados con solo un par de lados paralelos.
bases (b₁, b₂)bases (b₁, b₂)
The two parallel sides of a trapezoid.Los dos lados paralelos de un trapecio.
heightaltura
The straight-up distance between the two parallel bases.La distancia recta entre las dos bases paralelas.
decomposedescomponer
Break a figure into simpler shapes.Separar una figura en figuras más simples.

Stage 1 of 5Etapa 1 de 5

Start StrongEmpieza fuerte

Each rung is harder than the last, and the numbers change every time.

Cada peldaño es más difícil que el anterior y los números cambian cada vez.

  1. 6 fresh problems with new numbers each time (interactive only).

Stage 2 of 5Etapa 2 de 5

Stretch Your ThinkingAmplía tu pensamiento

Plan, solve, then check that your answer makes sense.

Planea, resuelve y revisa que tu respuesta tenga sentido.

  1. Find the Area Error
  2. A trapezoid and a parallelogram both have a height of 8 ft. The trapezoid has bases of 5 ft and 11 ft. The parallelogram has a base of 7 ft. Which shape has the greater area? Explain your reasoning using the formulas.
  3. A coral nursery bed is a trapezoid with parallel bases of 14 m and 6 m and a height of 5 m. Shade net costs $8 per square meter. How many dollars does the net for one bed cost?
  4. A trapezoid-shaped lagoon plot has an area of 75 m², a height of 5 m and one base of 11 m. What is the length of the other base?
    • 15 m
    • 19 m
    • 30 m
    • 64 m
  5. Three tide-pool trays are trapezoids. Find each missing value, then add the three areas in the Total row.
  6. Two identical trapezoid reef panels have bases of 5 m and 9 m and a height of 4 m. A diver flips one panel and joins it to the other to make a parallelogram. What is the area of ONE trapezoid panel?
    • 56 m²
    • 36 m²
    • 28 m²
    • 14 m²

Stage 3 of 5Etapa 3 de 5

InvestigateInvestiga

Use the model to test an idea. Then check it.

Usa el modelo para probar una idea. Luego compruébala.

  1. A trapezoid has bases of 6 and 10 and a height of 4. Sort each calculation by whether it finds the correct area or has a mistake.
  2. Design two different trapezoids that both have an area of 60 square units. Label the two bases and the perpendicular height of each. Show ½ × (b1 + b2) × h for both, and explain why different shapes can have the same area.
  3. 4 fresh problems with new numbers each time (interactive only).

Stage 4 of 5Etapa 4 de 5

Find and FixEncuentra y corrige

Somebody made a mistake. Find the step and fix it.

Alguien cometió un error. Encuentra el paso y corrígelo.

  1. A reef ramp is a trapezoid with bases of 9 m and 15 m, a height of 4 m and a sloping side of 5 m. Rosa finds its area. Tap the first step where her work goes wrong.
  2. A trapezoid window for the reef lab has bases of 12 ft and 8 ft and a height of 7 ft. Kai finds its area. Tap the first step where his work goes wrong.
  3. A trapezoid has an area of 60 m², a height of 6 m and one base of 8 m. Noa finds the other base. Tap the first step where her work goes wrong.
  4. A trapezoid has bases of 4 m and 10 m and a height of 5 m. Lola says you can multiply the average of the two bases by the height to get the area. Pablo says that only works for rectangles. Who is right?
    • Pablo. Averages only work for rectangles.
    • Neither. You must multiply the two bases together.
    • Lola, but only if the trapezoid has a right angle.
    • Lola; the average base is 7, and 7 × 5 = 35 m².
  5. What is the best next move?
    • Divide 108 by 6 and subtract 10.
    • Divide 108 by 10 to find the other base.
    • Double 108 ÷ 6, then subtract 10.
    • Subtract 10 from 108, then take half.

Stage 5 of 5Etapa 5 de 5

Prove Your UnderstandingDemuestra tu comprensión

Say how sure you are, solve, then create a problem of your own.

Di qué tan seguro estás, resuelve y luego crea un problema tuyo.

  1. A turtle-nesting shade is a trapezoid with bases of 12 ft and 8 ft and a height of 7 ft. What is its area, in square feet?
  2. A trapezoid has bases of 5 m and 11 m and a height of 6 m. Which expression gives its area?
    • ½ × (5 + 11) × 6
    • ½ × 5 × 11 × 6
    • (5 + 11) × 6
    • ½ × (5 + 11 + 6)
  3. A trapezoid-shaped lagoon has an area of 90 m² and bases of 13 m and 17 m. What is its height, in meters?
  4. A reef ramp is a trapezoid with bases of 10 m and 16 m and a height of 4 m. One can of reef-safe paint covers 8 m². How many cans does the crew need to paint one ramp?
  5. A trapezoid has bases of 4 m and 6 m and a height of 3 m. A bigger trapezoid has both bases doubled and the same height. What happens to the area?
    • It stays the same
    • It doubles, from 15 m² to 30 m²
    • It becomes 4 times as large
    • It increases by 10 m²
  6. Create your own Reef Rescue problem about a trapezoid. Give two bases and a height, find the area, and explain why you add the bases and take half.