Grade 6 Area and Perimeter Worksheets | Free Math Worksheets - Free Printable

Let's solve each of the composite shapes step by step and find their areas.

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Problem 1:

Shape Description:
This is a "T-shaped" figure made up of two rectangles:
- A horizontal rectangle at the bottom (8m wide, 2m high)
- A vertical rectangle on top (2m wide, 8m high)

But wait — let’s analyze carefully.

Looking at the diagram:

- The bottom rectangle is 8m wide and 2m tall.
- The top rectangle is 2m wide and 8m tall. But it sits centered on top of the bottom rectangle.

Wait — this seems inconsistent because if the top part is 2m wide and 8m tall, and the bottom is 8m wide and 2m tall, then the total height is not matching.

Let’s re-express the shape based on standard interpretation.

Actually, from the image:

- The total width of the base is 8m.
- The height of the bottom rectangle is 2m.
- On top of that, there is a central column of width 2m, extending up 8m in total?

Wait — but the label says "8m" next to the vertical side of the top part.

Let’s interpret correctly:

It looks like:
- The bottom rectangle is 8m wide × 2m high.
- The top rectangle is 2m wide × 8m high? That would make the total height 10m, but that doesn't make sense.

Wait — actually, looking again:

The vertical line labeled "8m" goes from the top of the bottom rectangle up to the top of the shape. So the total height of the shape is 8m.

But the bottom rectangle is only 2m high, so the top rectangle must be 6m high?

Wait — no, the label "8m" is on the side of the top rectangle, suggesting its height is 8m.

But that can't be — because the bottom rectangle is only 2m high, and the total shape height would be more than 8m.

Wait — perhaps the 8m is the length of the vertical side of the top rectangle, meaning the top rectangle is 2m wide and 8m tall?

But that would make the entire shape very tall.

Wait — maybe I misread.

Let me reinterpret with care.

From the diagram:

- The bottom rectangle has:
- Width = 8m
- Height = 2m

- The top rectangle sits on top of the center of the bottom one.
- Width = 2m
- Height = 8m

But then the total height is 2m + 8m = 10m, which might be possible.

But the label "8m" is shown vertically next to the top rectangle, so yes, its height is 8m.

So:

- Bottom rectangle: 8m × 2m → Area = 8 × 2 = 16 m²
- Top rectangle: 2m × 8m → Area = 2 × 8 = 16 m²

Total area = 16 + 16 = 32 m²

✔ Answer for #1: 32 m²

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Problem 2:

Shape Description:
A composite shape made of:
- A rectangle at the bottom: 6m wide, 3m high
- A triangle on top: base = 6m, height = 4m

We are given:
- Rectangle: 6m × 3m → Area = 6 × 3 = 18 m²
- Triangle: Area = (base × height)/2 = (6 × 4)/2 = 24/2 = 12 m²

Total area = 18 + 12 = 30 m²

✔ Answer for #2: 30 m²

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Problem 3:

Shape Description:
An "L-shaped" figure.

We can split this into two rectangles.

Let’s break it down:

Option 1: Split into:
- Left rectangle: 8m high × 2m wide → Area = 8 × 2 = 16 m²
- Right rectangle: 3m high × (6m – 2m) = 3m × 4m = 12 m²

Wait — the total width is 6m, and the left part is 2m wide, so the right part is 6 – 2 = 4m wide.

But the height of the right rectangle is only 3m, while the left is 8m.

So:
- Left rectangle: 2m × 8m = 16 m²
- Right rectangle: 4m × 3m = 12 m²

Total area = 16 + 12 = 28 m²

Alternatively, you could split differently:
- Bottom rectangle: 6m × 3m = 18 m²
- Top rectangle: (8 – 3)m × 2m = 5m × 2m = 10 m² → Total = 18 + 10 = 28 m²

Same result.

✔ Answer for #3: 28 m²

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✔ Final Answers:

1. Area = 32 m²
2. Area = 30 m²
3. Area = 28 m²

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🔍 Explanation Summary:

For composite shapes, we break them into simpler shapes (rectangles, triangles), calculate each area separately, then add them together.

- Rectangle area: length × width
- Triangle area: (base × height)/2

Always check dimensions carefully and ensure units are consistent.

Let me know if you'd like a visual breakdown!