Math · Stage 5

Dissect areas and count regions in composite figures

Two Olympiad moves for messy shapes: DISSECT a composite figure into rectangles (or subtract a cut-out notch) to find its area, and COUNT every region a set of lines makes — small pieces first, then the bigger shapes they build.

✦ Math📘 Stage 5 · S5⏱ ~12 min🧒 Ages 9–10★ Free to start

I can dissect areas and count regions in composite figures.

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Kavi the Shape-Cutter ✂️

Kavi finds a wonky L-shaped garden and a window criss-crossed with lines. "I can't measure a bendy shape all at once," hoots Kavi, "so I slice it into neat rectangles, measure each, and add them up. And where lines cross and overlap, I count every region carefully — small pieces first — so I never miss one 🔍."

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What your child will learn

1Slice the L into two neat rectanglesA composite figure is just simple shapes stuck together. Cut this L along the dashed line and it falls into two rectangles. Tap each part to see its area.

2Add the pieces — or subtract the notchThe same L-shape (from the last page) has two tidy methods. Tap each card.

3Count small pieces first, then the bigger shapesWhen lines cross a figure, don't just count the little pieces — count every bigger shape they join into, too. Make a guess, then tap to check.

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A peek inside

Find the area of an L-shape made of a 2×4 rectangle joined to a 3×2 rectangle (in square units).

dissect and add: 2×4 = 8, 3×2 = 6, then 8 + 6

Try this at home: Add the pieces: an L-shape is a 5×2 rectangle plus a 2×3 rectangle. Area = 5×2 + 2×3 = __ square units

Ready to play and learn?

Start the free interactive lesson, or print the handout for screen-free play.

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Part of Math · Stage 5 · S5 on KAVI Academy — a secular, whole-child learning platform for ages 5–12.