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Mathable Smart Lab

CLASS VIII • AREASmart Lab: Areas, Dissections & Shape Reasoning

Area: Shapes, Formulas and Dissections

Explore area as unit squares, compare area and perimeter, calculate areas of rectangles, triangles, parallelograms, rhombi and trapezia, and dissect shapes into equal-area pieces.

Fact Sheet: What Area Measures

Area measures how much surface a region covers. We count how many unit squares fit inside a shape.

Rectangle: A 7 cm by 4 cm rectangle contains 7 × 4 = 28 unit squares, so its area is 28 cm².
Triangle: A diagonal splits a rectangle into two congruent triangles. Each triangle has half the area of the rectangle.
Important idea: Perimeter is boundary length. It is not a measure of area. Two shapes can have the same perimeter but different areas.
7 × 4 = 28 cm²Triangle = ½ rectangleSame perimeter? Area can differ!

Formula Hub

Rectangle

Area = length × width

A = l × w

Square

Area = side × side

A = s²

Triangle

Area = half of base × height

A = ½ × b × h

Parallelogram

Dissect and rearrange into a rectangle.

A = b × h

Rhombus

Use diagonals or base-height.

A = ½ × d₁ × d₂

Trapezium

Average of parallel sides × height.

A = ½ × (a+b) × h

Polygon

Divide the polygon into triangles and add their areas.

Path Around Rectangle

Path area = outer rectangle area − inner rectangle area.

Area is preserved when a shape is cut and rearranged without overlap or gap.

Interactive Lab: Area Challenge

Score: 0Current Streak: 🔥 0Badge: Area Explorer


Activity Zone

📐 Shape Area Calculator

Choose a shape and enter its measurements.

🧱 Perimeter vs Area Explorer

Compare two rectangles. Notice how perimeter and area tell different stories.

🛣️ Path Area Around a Park

Find the area of a uniform path around a rectangular park.

🧩 Equal-Area Dissection Simulator

A square can be divided into four equal parts in many ways. Try changing the bend amount.

The four parts remain equal when each part is compressed and expanded by the same amount.

🔺 Triangle from Rectangle Visual

See why a triangle with the same base and height as a rectangle has half the area.

Worksheet Generator

Generate practice on rectangles, triangles, parallelograms, paths, unknown lengths, and area reasoning.



Real-World Use

Rangoli and Painting: Area helps estimate how much colour, paint, or powder is needed.
Gardens and Paths: Subtract inner area from outer area to find the area of a walkway.
Construction: Parallelogram, trapezium, and triangle formulas help estimate land, flooring, roofs, and tiles.

🌍 Real-Life Case Generator

Teacher Tools

Learning Outcomes

  • Measure area using unit squares.
  • Distinguish area from perimeter.
  • Derive and apply area formulae for rectangles, triangles, parallelograms, rhombi and trapezia.
  • Use dissection to transform shapes without changing area.
  • Decompose polygons into triangles to find area.

Exit Ticket Prompts

  • Give two rectangles with the same perimeter but different areas.
  • Explain why triangle area is half of base × height.
  • Find the area of a rectangular path around a park.
  • Describe how a parallelogram can be rearranged into a rectangle.