Determine the Area of Parallelograms and Rhombuses Challenge

Grade 6 Math · Unit 5 Challenge Studio (6.GR.1) · Lesson 5-1
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I can find the area of a parallelogram using base × height.Puedo hallar el área de un paralelogramo usando base × altura.

MissionMisión · Summit TrailSendero a la cumbre · night shiftturno de noche

Every checkpoint gets you higher.Cada punto de control te lleva más alto.

Night hike: headlamps are on, and the last checkpoints still need their platforms and trail markers measured. Find each area with the perpendicular height before the summit sunrise.

Caminata nocturna: las linternas están encendidas y a los últimos puntos de control todavía les faltan sus plataformas y señales por medir. Halla cada área con la altura perpendicular antes del amanecer en la cumbre.

Word bankBanco de palabras 4 words4 palabrasparallelogram, base, height, …paralelogramo, base, altura, …
parallelogramparalelogramo
A four-sided shape with two pairs of parallel sides.Una figura de cuatro lados con dos pares de lados paralelos.
basebase
Any side of a parallelogram. The height is measured perpendicular to it.Cualquier lado de un paralelogramo. La altura se mide perpendicular a ella.
heightaltura
The perpendicular distance from the base to the opposite side. It is not the slanted side.La distancia perpendicular desde la base hasta el lado opuesto. No es el lado inclinado.
rhombusrombo
A parallelogram with four sides of the same length.Un paralelogramo con cuatro lados de la misma longitud.

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 parallelogram has a base of 12 cm. If you double the height, the area doubles too. Explain why this happens using the formula, and give a specific example with numbers.
  3. The trail crew builds a camp platform shaped like a parallelogram. Its base is 12 m, its height is 5 m, and its slanted side is 7 m. One bag of gravel covers 4 m². How many bags cover the platform?
  4. A parallelogram solar panel has an area of 84 m² and a base of 12 m. Hikers will set it under a rock ledge with 6 m of clearance. Will the panel fit under the ledge?
    • Yes, its height is 72 m
    • No; height 7 m > 6 m.
    • No, its height is 14 m
    • Yes, its height is 5 m
  5. Three camp terraces are parallelograms. Find each missing value, then add the three areas in the Total row.
  6. A trail marker is a rhombus with sides of 10 cm and a perpendicular height of 8 cm. What is its area?
    • 18 cm²
    • 40 cm²
    • 80 cm²
    • 100 cm²

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. Each trail shape lists a base, a slanted side and a height. Match each shape to its area.
  2. Design two different parallelogram gardens that both have an area of 48 square units. Give each one a base, a perpendicular height and a slanted side. Explain how you know the areas are equal even though the shapes look different.
  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 trail map shows a parallelogram with base 15 ft, slanted side 13 ft and height 12 ft. Gabi finds its area. Tap the first step where her work goes wrong.
  2. A tent floor is a parallelogram with base 7 ft and height 4 ft. Hamza finds the area. Tap the first step where his work goes wrong.
  3. A parallelogram has an area of 72 m² and a base of 8 m. Pilar finds its height. Tap the first step where her work goes wrong.
  4. A parallelogram has sides of 12 ft and 8 ft. The height to the 12-ft side is 6 ft. The height to the 8-ft side is 9 ft. Luis says use the longer side as the base. Aiko says any side works with its own height. Who is right?
    • Luis. Only the longer side can be the base.
    • Luis. Using the 8-ft side gives a smaller area.
    • Aiko. The areas are different, so use the biggest.
    • Aiko. Both choices give the same area, 72 ft².
  5. What is the best next move?
    • Divide 154 by 14 to find the height.
    • Take half of 154, then divide by 14.
    • Subtract 14 from 154 to find the height.
    • Multiply 154 by 14 to find the height.

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 rest area on the trail is a parallelogram with a base of 18 m and a height of 7 m. What is its area, in square meters?
  2. A sign at the summit is a parallelogram with a base of 9 cm and a height of 5 cm. Which answer has the correct number and unit for its area?
    • 45 cm
    • 45 cm²
    • 14 cm²
    • 45 cm³
  3. A tent floor is a parallelogram with a base of 6 ft and a height of 4 ft. A bigger tent has a base 3 times as long and the same height. What is the area of the bigger tent?
  4. A parallelogram garden bed has an area of 135 ft² and a height of 9 ft. What is the length of its base, in feet?
  5. Two parallelogram pads: Pad 1 has a base of 11 m, a height of 6 m and a slanted side of 12 m. Pad 2 has a base of 8 m, a height of 8 m and a slanted side of 10 m. Which pad is larger?
    • Pad 1, by 2 m²
    • Pad 1, by 52 m²
    • Pad 2, because its base and height are equal
    • They have equal areas
  6. Create your own Summit Trail problem about a parallelogram. Give a base, a height and a slanted side, find the area, and explain why the slanted side is not used.