Area Unlocked — ESOL Edition

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Estación 1 — Explorar / Station 1 — Explore

Area Is Everywhere

Activate your thinking. Find these shapes in the real world before we find formulas.

Standards 6.G.A.1 Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes.

🌍 Real World Connection

Where do you see these shapes?

◆A parallelogram — like a slanted tile floor, a street sign, or a solar panel array

◆A rhombus — like a baseball diamond, a kite, or a decorative floor pattern

◆A triangle — like a roof truss, a traffic sign, a pizza slice, or a sail

🔍 What Do You Notice? Click each shape to learn what makes it unique

Parallelogram

Opposite sides parallel

Rhombus

All sides equal

Triangle

Three sides, three angles

📚 Key Vocabulary

⭐ Cognates: Words that look similar in English & Spanish!

área→ area ✓ base→ base ✓ perpendicular→ perpendicular ✓ diagonal→ diagonal ✓ fórmula→ formula ✓ triángulo→ triangle ✓ paralelogramo→ parallelogram ✓

Term / Término	Student-Friendly Meaning / Significado	Example / Ejemplo	🇪🇸 Español + Cognate?
Area	The number of square units needed to cover the inside of a shape	How many 1×1 tiles fit inside?	Área
Base (b)	The bottom side of a shape — the side the height is measured from	Any side can be the base if you rotate the shape	Base
Height (h)	The perpendicular distance from the base to the opposite side or vertex — always straight up	Height must form a 90° right angle with the base	Altura
Perpendicular	Lines that meet at exactly 90° (a right angle)	Height is ALWAYS perpendicular to the base	Perpendicular
Diagonal (d)	A line connecting two opposite corners of a shape	A rhombus has two diagonals that cross at 90°	Diagonal
Decompose	To break a shape into smaller, simpler shapes to find its area	A parallelogram = rectangle when you move the triangle piece	Descomponer

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Estación 2 — Descubrir / Station 2 — Discover

Build the Formulas

Use the interactive sliders to see how changing dimensions changes area — then discover why the formulas work.

🗣️ Key Math Phrases / Frases Clave

"The area is…"
"El área es…"

"I multiply base times height"
"Multiplico base por altura"

"I divide by two because…"
"Divido entre dos porque…"

"The formula for ___ is…"
"La fórmula para ___ es…"

"The height is perpendicular to…"
"La altura es perpendicular a…"

"This shape has ___ sides"
"Esta figura tiene ___ lados"

Parallelogram

A = b × h

base × perpendicular height

Rhombus

A = (d₁ × d₂) ÷ 2

half the product of diagonals

Triangle

A = (b × h) ÷ 2

half of base × height

🟦 Parallelogram Why A = b × h

Slide the sliders to change the base and height. Watch the area update. Notice: the slant side doesn't matter — only the height and base do!

Base (b) = 8 units

Height (h) = 5 units

Area = b × h

square units

💬 Write About It (TWR) — Choose a sentence frame below

The area of a parallelogram is found by multiplying the base and height because , similar to how .

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Worked Example — Parallelogram

Identify the formula

To find the area of a parallelogram, use A = b × h. Remember: use the perpendicular height, not the slant side.

Label the dimensions

A parallelogram has base = 12 cm and height = 7 cm (the slant side = 9 cm — do not use this).

b = 12 cm h = 7 cm

Substitute and solve

Multiply base times height.

A = 12 × 7 = 84 cm²

Check your units

Area is always in square units — cm², m², in², ft². Don't forget the ² exponent!

💎 Rhombus Why A = (d₁ × d₂) ÷ 2

The two diagonals of a rhombus divide it into 4 right triangles. Together they form a rectangle — and the rhombus is exactly half of it!

Diagonal 1 (d₁) = 10 units

Diagonal 2 (d₂) = 6 units

Area = (d₁ × d₂) ÷ 2

square units

💬 Write About It (TWR)

The rhombus formula uses diagonals instead of base and height because . This gives the same result as .

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Worked Example — Rhombus

Identify the formula

A rhombus area uses its two diagonals: A = (d₁ × d₂) ÷ 2. The diagonals are the lines connecting opposite vertices.

Label the diagonals

A baseball diamond (rhombus) has diagonals of 127 ft and 127 ft.

d₁ = 127 ft d₂ = 127 ft

Multiply and halve

A = (127 × 127) ÷ 2 = 16,129 ÷ 2 = 8,064.5 ft²

🔺 Triangle Why A = (b × h) ÷ 2

Every triangle is exactly half of a parallelogram! If you copy the triangle and flip it, the two pieces form a parallelogram — so triangle area is always half of b × h.

Base (b) = 10 units

Height (h) = 6 units

Area = (b × h) ÷ 2

square units

💬 Write About It (TWR)

A triangle's area formula includes "÷ 2" because . This is connected to the parallelogram formula because .

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Worked Example — Triangle (Tricky! Obtuse)

Watch out: height is outside the triangle!

For an obtuse triangle, the height is drawn outside the triangle. The formula still works the same way: A = (b × h) ÷ 2.

Identify base and height

Base = 14 m (the bottom side). Height = 9 m (the perpendicular line — even though it falls outside the triangle).

b = 14 m h = 9 m

Substitute and solve

A = (14 × 9) ÷ 2 = 126 ÷ 2 = 63 m²

⚠️ Common error to avoid

Students often use the slant side as the height. Remember: height must be perpendicular to the base — it always forms a right angle (90°).

🔗 The Big Connection

All three formulas connect back to the area of a rectangle. A parallelogram is a rearranged rectangle. A triangle is half of a parallelogram. A rhombus uses diagonals to find the same half-rectangle relationship.

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Estación 3 — Practicar / Station 3 — Practice

Put It to Work

12 problems across three tiers. Type your answer and click Check — you'll get immediate feedback.

Correct

Total

Score

🌐 Language Support / Apoyo de Lenguaje

L1–2 Entering/Emerging

Point to the shape. Circle the formula. Write the numbers. Use a calculator.
Señala la figura. Encierra la fórmula.

L3–4 Developing/Expanding

Use the sentence frames below each problem. Write each step. Say your answer: "The area is ___ square ___."
Usa los marcos de oraciones. Escribe cada paso.

L5 Bridging

Explain your reasoning in writing. Compare two shapes. Use math vocabulary in your explanation.
Explica tu razonamiento por escrito.

🗝️ Math Word Bank / Banco de Palabras

area / área base / base height / altura multiply / multiplicar divide / dividir formula / fórmula perpendicular diagonal / diagonal square units / unidades cuadradas parallelogram / paralelogramo rhombus / rombo triangle / triángulo

Tier 1 Single-step — identify the shape and apply the formula

Parallelogram

📐 Parallelogram / Paralelogramo — a 4-sided shape with 2 pairs of parallel sides (lados paralelos)

Find the area of the parallelogram.
Encuentra el área del paralelogramo.
Base = 14 cm, Height / Altura = 9 cm.

🗣️ "The formula for a parallelogram is A = ___ × ___. So the area is ___ cm²."

cm²

✏️ Show Your Work (type here)

Hint: The formula for a parallelogram is A = b × h. Multiply the base (14) by the height (9). Don't use the slant side!

Rhombus

💎 Rhombus / Rombo — all 4 sides equal length (todos los lados iguales). Uses diagonals (diagonales).

A rhombus kite has diagonals of 16 m and 10 m. What is the area?
Un cometa tiene diagonales de 16 m y 10 m. ¿Cuál es el área?

🗣️ "The formula for a rhombus is A = (d₁ × d₂) ÷ 2. I multiply ___ × ___ = ___, then divide by 2."

m²

✏️ Show Your Work (type here)

Hint: Rhombus formula: A = (d₁ × d₂) ÷ 2. Multiply both diagonals (16 × 10 = 160), then divide by 2.

Triangle

🔺 Triangle / Triángulo — 3 sides. Area = HALF of base × height (la MITAD de base × altura)

A triangular garden (jardín triangular) has base = 18 ft and height (altura) = 11 ft. Find the area.
Encuentra el área del jardín triangular.

🗣️ "A triangle is half of a parallelogram, so I multiply ___ × ___ = ___, then divide by ___."

ft²

✏️ Show Your Work (type here)

Hint: Triangle formula: A = (b × h) ÷ 2. Multiply base × height = 18 × 11 = 198, then divide by 2.

Parallelogram

⚠️ Trap! / ¡Trampa! — The slant side is NOT the height. Look for the right angle (ángulo recto = 90°) to find the real height.

A parallelogram tile has base 13 cm, slant side (lado inclinado) 10 cm, and height 7.5 cm.
¿Cuál es el área? No uses el lado inclinado.

🗣️ "I use A = b × h. The base is ___, the HEIGHT (not the slant side) is ___. Area = ___."

cm²

✏️ Show Your Work (type here)

Hint: Don't use the slant side (10 cm)! Only use the base and the perpendicular height. A = b × h = 13 × 7.5

Tier 2 Multi-step — apply and reason

Missing Dimension

A triangle has an area of 48 in² and a base of 12 in. What is the height?

Strategy Frame

I know the formula A = (b × h) ÷ 2, so I can work backwards. If A = 48 and b = 12, then h = because .

✏️ Show Your Work (type here)

Hint: Start with A = (b × h) ÷ 2. Plug in: 48 = (12 × h) ÷ 2. Multiply both sides by 2: 96 = 12 × h. Then divide: h = 96 ÷ 12.

Real World

A diamond-shaped window (rhombus) has a horizontal diagonal of 2.4 ft and a vertical diagonal of 3.6 ft. A replacement window costs $18 per ft². What is the total cost?

dollars

✏️ Show Your Work (type here)

Hint: Step 1: Find the area of the rhombus: A = (2.4 × 3.6) ÷ 2. Step 2: Multiply area × $18.

Missing Dimension

A parallelogram has an area of 91 m² and a height of 7 m. What is the base?

✏️ Show Your Work (type here)

Hint: A = b × h → 91 = b × 7 → b = 91 ÷ 7.

Composite

A rooftop is shaped like a triangle with base 24 m and height 6.5 m. Solar panels cover ⅔ of the roof. What area do the solar panels cover?

m²

✏️ Show Your Work (type here)

Hint: Step 1: Triangle area = (24 × 6.5) ÷ 2 = 78 m². Step 2: ⅔ of 78 = 78 ÷ 3 × 2 = 52 m².

Tier 3 Transfer + justification — DOK 3

Compare & Contrast

A parallelogram has base 10 cm and height 8 cm. A triangle has the same base and height. How many triangles are needed to cover the same area as the parallelogram?

triangles

✏️ Show Your Work (type here)

Hint: Find the area of each. Parallelogram: A = 10 × 8 = 80 cm². Triangle: A = (10 × 8) ÷ 2 = 40 cm². How many 40s fit in 80?

💬 Explain Your Thinking (TWR)

The triangle formula includes ÷ 2 because it is exactly _____ the area of the parallelogram with the same dimensions. This means _____ triangles always equal one parallelogram.

Error Analysis

Marcus says: "A triangle with base 8 and height 5 has area 40 square units. I just did 8 × 5." What is Marcus's error? What is the correct area?

sq units

✏️ Show Your Work (type here)

Hint: Marcus used the parallelogram formula, not the triangle formula. Triangle area = (b × h) ÷ 2, not just b × h.

💬 Error Explanation (TWR)

Marcus's mistake was that he _______________. The correct formula is _______________. The right answer is _______ because _____________.

Transfer

A rhombus and a rectangle have the same area. The rectangle is 9 cm × 8 cm. The rhombus has one diagonal of 12 cm. What is the length of the other diagonal?

✏️ Show Your Work (type here)

Hint: Step 1: Rectangle area = 9 × 8 = 72 cm². Step 2: Set rhombus formula equal: (12 × d₂) ÷ 2 = 72. Step 3: Solve for d₂.

Open-Ended

You need to cover a triangular floor with tiles. The triangle has base 15 ft and height 8 ft. Tiles come in 1 ft² squares. If tiles cost $3.50 each, what is the minimum cost to tile the floor? (You can't cut tiles.)

dollars

✏️ Show Your Work (type here)

Hint: Step 1: Triangle area = (15 × 8) ÷ 2 = 60 ft². Step 2: Since you can't cut tiles, you need 60 tiles. Step 3: Cost = 60 × $3.50.

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Estación 4 — Desafío / Station 4 — Challenge

Think Deeper

DOK 3 tasks — decompose, design, and justify. Show your thinking.

📐 Design Space Parallelogram with A = 60 ft²

There are infinite possible answers. Choose base and height that multiply to 60.

My base =

My height =

Computed area =

—

🔺 Design Space Triangle with A = 60 ft²

For a triangle, (b × h) ÷ 2 = 60, so b × h = 120.

My base =

My height =

Computed area =

—

🔍 Decompose This Complex Shape Challenge

This building cross-section is made of a parallelogram (base = 140, height = 80) sitting under a triangle (base = 140, height = 60). All units in feet.

Find the total area of the cross-section. Show your work below.

ft²

✍️ Justify Your Reasoning (TWR)

Frame 1 — Explain the Connection

The triangle formula is half of the parallelogram formula because ________________________. I can prove this by ________________________.

Frame 2 — Apply to Decomposition

When a complex shape is decomposed into simpler shapes, the total area equals ________________________ because ________________________.

Frame 3 — Compare Formulas

The rhombus diagonal formula and the parallelogram base-height formula are similar because ________________________, but different because ________________________.

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Estación 5 — Reflexionar / Station 5 — Reflect

Show What You Know

Complete the exit ticket and rate your confidence. This is the printable section.

📊 Track Your Journey

🔭

Explore

🔬

Discover

✏️

Practice

⚡

Challenge

🎯

Reflect

🎯 Goal Self-Assessment How well can you find areas of these shapes?

I need more time. The formulas are new to me.
Necesito más tiempo.

I can do it with hints or by looking at the formulas.
Puedo hacerlo con ayuda.

I can solve most problems on my own.
Puedo resolver solo/a.

I can teach this and use it in new ways.
Puedo enseñarlo y aplicarlo.

Reflection TWR

My goal level is _____ because _____________________________. One thing I still want to practice is _____________________________.

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Exit Ticket — Area of Parallelograms, Rhombuses & Triangles

6.G.A.1 · Neft.Alba · EduWonderLab

Name

Period

Date

⭐ Tier 1 — Identify

A parallelogram has base = 11 cm and height = 6 cm. Which formula applies, and what is the area?

⭐⭐ Tier 2 — Explain

A triangle and a parallelogram share the same base and height. Explain why the triangle's area is exactly half the parallelogram's area. Use a TWR sentence to justify.

TWR Stem

The triangle formula includes ÷ 2 because , which is similar to .

⭐⭐⭐ Tier 3 — Transfer

A rhombus has an area of 84 in². One diagonal measures 14 in. Find the other diagonal. Then explain: could a triangle with the same diagonals as lengths have the same area? Why or why not?

Captures your answers, TWR responses & score

EduWonderLab — Area Unlocked HyperDoc

Grade 6 · CCSS 6.G.A.1 · Interactive Digital Activity · Neft.Alba