This printable worksheet helps students practice calculating the area of composite rectangles by breaking down complex shapes into simpler parts.

Let’s solve each problem step by step. We’ll break each composite shape into rectangles, find the area of each rectangle, then add them up.

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Problem 1:
Shape is an L-shape.
Break it into two rectangles:
- Left vertical part: width = 5 ft, height = 20 ft → Area = 5 × 20 = 100 sq ft
- Top horizontal part (excluding the overlapping part): length = 30 - 5 = 25 ft, height = 15 ft → Area = 25 × 15 = 375 sq ft
Total Area = 100 + 375 = 475 sq ft

Wait — let me double-check. Actually, another way:
Top rectangle: 30 ft long × 15 ft high = 450 sq ft
Bottom left rectangle: 5 ft wide × (20 - 15) = 5 ft high → 5 × 5 = 25 sq ft
Total = 450 + 25 = 475 sq ft ✔

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Problem 2:
This is a big rectangle with a small rectangle cut out from the middle-left.
Big rectangle: 25 cm wide × 30 cm tall = 750 sq cm
Cut-out rectangle: 5 cm wide × (30 - 10 - 10) = 10 cm tall? Wait — look at diagram:
Left side has two 10 cm segments and a 5 cm gap in between vertically? Actually, the cutout is 5 cm wide and its height is 30 - 10 - 10 = 10 cm? Let's see:

Actually, the shape is like a “C” on its side? No — looking again:

It’s a large rectangle 25 cm wide × 30 cm tall, but there’s a rectangular notch on the left side that is 5 cm wide and goes from y=10 to y=20? So height of notch = 10 cm.

So area removed = 5 × 10 = 50 sq cm
Total area = 750 - 50 = 700 sq cm

Alternatively, split into three parts:
- Top rectangle: 25 × 10 = 250
- Bottom rectangle: 25 × 10 = 250
- Middle right rectangle: (25 - 5) × 10 = 20 × 10 = 200
Total = 250 + 250 + 200 = 700 sq cm ✔

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Problem 3:
T-shaped figure upside down? Or just a rectangle with a smaller rectangle attached below center.

Main top rectangle: 36 m wide × 24 m tall? But wait — total height isn’t given directly.

Looking: The bottom protrusion is 10 m wide and extends downward. The main body is 36 m wide and 24 m tall? But then the bottom part adds more height? Actually, no — the 24 m is the full height including the bottom part? Let me read labels.

Label says: overall width 36 m, overall height 24 m? But then bottom part is labeled 10 m wide and... how tall?

Actually, the figure shows:
- Top rectangle: 36 m wide, and height = ?
- Bottom rectangle: 10 m wide, and height = ?

But we’re told the total height is 24 m? And the bottom part sticks down — so perhaps the top part is 24 m minus the height of the bottom part? But bottom part height not given.

Wait — re-examining: The label “24 m” is on the right side, going from top to bottom of entire figure. The bottom protrusion is labeled “10 m” for width, but no height. However, the left side has a segment labeled “14 m” — which must be the height of the top part above the bottom protrusion.

Ah! So:
- Top rectangle: 36 m wide × 14 m high → Area = 36 × 14 = 504 sq m
- Bottom rectangle: 10 m wide × (24 - 14) = 10 m high → Area = 10 × 10 = 100 sq m
Total = 504 + 100 = 604 sq m

Check: 24 - 14 = 10, yes. So bottom part is 10 m tall. Correct.

✔ 604 sq m

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Problem 4:
T-shape upright.

Top bar: 12 ft wide × 6 ft high → Area = 72 sq ft
Stem: width = ? From diagram: stem is centered, and sides are 3 ft each, so stem width = 12 - 3 - 3 = 6 ft? Wait, no — actually, the stem is drawn as having width such that the overhangs are 3 ft on each side? But the stem height is 8 ft.

Actually, looking: the top rectangle is 12 ft wide × 6 ft high.
The stem is below it, and its width is not labeled, but the horizontal distances from edge to stem are both 3 ft, so stem width = 12 - 3 - 3 = 6 ft.
Height of stem = 8 ft.
Area of stem = 6 × 8 = 48 sq ft
Total = 72 + 48 = 120 sq ft

But wait — is the stem really 6 ft wide? The diagram shows "3 ft" on left and right of the stem under the top bar, so yes, stem width = 12 - 3 - 3 = 6 ft.

✔ 120 sq ft

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Problem 5:
H-shape or I-beam shape.

We can think of it as:
- Top rectangle: 14 yd × 8 yd? No — wait, the top part is 14 yd long and 8 yd high? But then there are indentations.

Better to split into three horizontal rectangles:
- Top: 14 yd × 8 yd? But no — the 8 yd is the height of the top and bottom bars, and the middle bar is also 8 yd high? That doesn't make sense.

Look at labels:
Overall width = 14 yd
Top bar height = 8 yd
Bottom bar height = 8 yd
Middle bar height = 8 yd? But then total height would be 24 yd, but no label for that.

Actually, the vertical dimension: the top bar is 8 yd high, then there’s a gap, then middle bar 8 yd high, then gap, then bottom bar 8 yd high? But the gaps are labeled 5 yd each? No — the 5 yd is the width of the indentations.

Actually, standard way: this shape is made of three rectangles:
- Top: 14 yd × 8 yd = 112
- Bottom: 14 yd × 8 yd = 112
- Middle: the connecting part — but it’s indented on both sides by 5 yd, so width = 14 - 5 - 5 = 4 yd, and height = 8 yd → 4 × 8 = 32
Total = 112 + 112 + 32 = 256 sq yd

Is that correct? Let me visualize: yes, like an H rotated 90 degrees? No, it's like a capital I with thick flanges.

Another way: imagine full rectangle 14 yd wide × (8+8+8)=24 yd high = 336 sq yd, then subtract the two side cutouts.

Each cutout is 5 yd wide × 8 yd high (the gaps between top/middle and middle/bottom). There are two cutouts per side? Actually, on left and right, between top and middle bar, and between middle and bottom bar — so four cutouts? No.

Actually, the shape has:
- Full height if solid: 8 (top) + 8 (middle) + 8 (bottom) = 24 yd
But the middle section is only 4 yd wide (since 5 yd cut out on each side), so the missing parts are two rectangles on left and two on right? Better to stick with addition.

I think my first method is correct: three separate rectangles:
Top: 14×8=112
Middle: (14-5-5)×8=4×8=32
Bottom:14×8=112
Sum: 256

✔ 256 sq yd

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Problem 6:
L-shape but oriented differently.

Can split into two rectangles:
Option 1:
- Large bottom rectangle: 28 m wide × 6 m high → 168 sq m
- Right vertical rectangle: width = 12 m, height = 18 - 6 = 12 m → 12 × 12 = 144 sq m
Total = 168 + 144 = 312 sq m

But wait — is the right part 12 m wide? Label says top right is 12 m, and total width is 28 m, so left part is 28 - 12 = 16 m? But the bottom is all 28 m.

Actually, better:
Split vertically:
- Left rectangle: width = 28 - 12 = 16 m, height = 6 m → 96 sq m
- Right rectangle: width = 12 m, height = 18 m → 216 sq m
Total = 96 + 216 = 312 sq m

Same answer.

Check with another split:
Horizontal:
- Bottom: 28 × 6 = 168
- Top right: 12 × (18 - 6) = 12 × 12 = 144
Sum: 312 ✔

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Problem 7:
F-shape or something similar.

Labels: overall height 8 mm, width 6 mm at top.
There are indentations.

Break into rectangles:
Method: start from left.

Vertical stem on left: width = ? Not labeled, but we can infer.

From diagram:
- Leftmost vertical part: height 8 mm, width = let's say W.
Then there are two horizontal arms to the right.

Actually, better to use coordinates or known dimensions.

Given:
Total height = 8 mm
Top arm: extends 6 mm right, height 2 mm
Then below that, a gap of 1 mm? Then a middle arm: extends 3 mm right, height 1 mm? Then gap 1 mm, then bottom arm: extends 3 mm right, height 1 mm? This is messy.

Alternative approach: calculate total bounding box minus cutouts.

Bounding box: 6 mm wide × 8 mm high = 48 sq mm

Now, what is cut out? On the right side, there are two rectangular holes.

From top:
After the top 2 mm, there is a region that is cut out: from x=3 to x=6 (width 3 mm), and y=2 to y=3 (height 1 mm)? Let's see labels.

Diagram shows:
- At top: 6 mm wide, 2 mm high → that's solid.
- Below that, on the right, there is a recess: labeled "3 mm" horizontally and "1 mm" vertically? Actually, the label "3 mm" is inside the recess, meaning the depth of the recess is 3 mm? And height of recess is 1 mm? Similarly below.

Actually, standard interpretation for such diagrams:

The shape consists of:
- A left vertical rectangle: width = 6 - 3 = 3 mm? No.

Let me define:

Assume the left edge is x=0.

From y=0 to y=8: there is a left part that is always present. Width of left part: since the top extends to 6 mm, and the recesses go in 3 mm, so left part width = 6 - 3 = 3 mm? But then the middle and bottom arms extend only 3 mm, which matches.

So:
- Left rectangle: 3 mm wide × 8 mm high = 24 sq mm
- Top arm: from x=3 to x=6 (3 mm wide), y=6 to y=8 (2 mm high) → 3×2=6 sq mm
- Middle arm: from x=3 to x=6? No, label says "3 mm" for the arm, but probably from x=3 to x=6 is 3 mm, but the arm might be shorter.

Looking at labels:
- After the top 2 mm, there is a 1 mm gap down, then a horizontal segment labeled "3 mm" — this is likely the length of the middle arm, so it extends 3 mm to the right from the left stem.
Similarly, after another 1 mm gap, bottom arm extends 3 mm.

And the left stem is continuous.

So:
- Left stem: width = ? Since top arm is 6 mm total, and it starts at left, so left stem must be at least the width where the arms attach.

Actually, the top arm is 6 mm long, so it includes the left stem? No, typically in such figures, the 6 mm is the total width at top, so the left stem is part of it.

Better: the shape has:
- A base rectangle on the left: let's say width W, height 8 mm.
- Attached to it on the right at top: a rectangle 3 mm wide (since 6-3=3? Confusing).

Use the given numbers:

From the diagram description:
- Total height: 8 mm
- Top projection: 6 mm wide, 2 mm high
- Then down 1 mm (gap)
- Then a horizontal part: 3 mm long, 1 mm high
- Then down 1 mm (gap)
- Then bottom horizontal part: 3 mm long, 1 mm high
- The left side is straight.

So, the left part is a rectangle that spans the full height 8 mm, and its width is the same as the starting point of the arms.

Since the top arm is 6 mm wide and it starts from the left, the left stem must have width such that when you add the arm, it's 6 mm. But the arm is attached to the stem, so if the stem is S mm wide, then the arm extends S + A = 6 mm? But the arm is labeled as extending 3 mm in the lower parts.

Perhaps the "6 mm" at top is the total width, and the stem is 3 mm wide, so the top arm extends 3 mm beyond the stem? But then the lower arms also extend 3 mm, so they align.

Yes, that makes sense.

So:
- Left stem: 3 mm wide × 8 mm high = 24 sq mm
- Top arm: 3 mm wide (extending right) × 2 mm high = 6 sq mm
- Middle arm: 3 mm wide × 1 mm high = 3 sq mm
- Bottom arm: 3 mm wide × 1 mm high = 3 sq mm
Total = 24 + 6 + 3 + 3 = 36 sq mm

But is the top arm only 2 mm high? Yes, labeled "2 mm" next to it.

And the gaps are 1 mm each, so positions:
- y=6 to 8: top arm (2 mm high)
- y=5 to 6: gap (1 mm)
- y=4 to 5: middle arm (1 mm high)
- y=3 to 4: gap (1 mm)
- y=0 to 3: bottom part? But bottom arm is only 1 mm high, so y=0 to 1: bottom arm, y=1 to 3: part of stem only.

In this case, the left stem is full height 8 mm, and the arms are additional.

So areas:
Stem: 3 * 8 = 24
Top arm: 3 * 2 = 6 (but this is on top of the stem? No, the stem is already included, so the arm is extra to the right.

In terms of area, since the stem is 3 mm wide, and the arms are attached to its right, so no overlap.

So total area = stem + top arm + middle arm + bottom arm = 24 + 6 + 3 + 3 = 36 sq mm

To verify, bounding box 6x8=48, minus the cutouts.

Cutouts: on the right side, between the arms.

From y=3 to y=4: a rectangle 3 mm wide (from x=3 to x=6) and 1 mm high? But at y=3 to 4, there is no arm, so it's empty.

Similarly, y=5 to 6: empty.

Also, from y=1 to y=3, only the stem is there, so from x=3 to 6 is empty for y=1 to 3? But the bottom arm is only at y=0 to 1.

Let's define regions:

For x from 0 to 3: always filled (stem) → area 3*8=24

For x from 3 to 6:
- y=6 to 8: filled (top arm) → 3*2=6
- y=4 to 5: filled (middle arm) → 3*1=3
- y=0 to 1: filled (bottom arm) → 3*1=3
- Other y: empty

So total for x>3: 6+3+3=12

Grand total: 24 + 12 = 36 sq mm ✔

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Problem 8:
Rectangle with a rectangular hole on the right side.

Outer rectangle: 16 cm wide × 28 cm high = 448 sq cm

Hole: on the right, labeled 6 cm wide and 18 cm high? But position: from bottom, it starts at some point.

Label says: at bottom, from left: 8 cm, then the hole is 6 cm wide, then presumably the rest.

Total width 16 cm, so if left part is 8 cm, hole is 6 cm, then right part is 16-8-6=2 cm? But the hole is cut out, so it's a void.

The hole is 6 cm wide and 18 cm high, and it's located such that from the bottom, it goes up 18 cm, and from the left, it starts at 8 cm? The label "8 cm" is under the left part, "6 cm" under the hole, so yes.

So hole area = 6 × 18 = 108 sq cm

Total area = outer - hole = 448 - 108 = 340 sq cm

Verify by splitting:
- Left rectangle: 8 cm × 28 cm = 224 sq cm
- Right rectangle: width = 16 - 8 - 6 = 2 cm? But the hole is 6 cm wide, so the material on the right of the hole is 2 cm wide, but only from y=18 to y=28? Because the hole is 18 cm high from bottom.

Actually, the shape is:
- From x=0 to 8: full height 28 cm → area 8*28=224
- From x=8 to 14 (6 cm): only from y=18 to 28 (10 cm high) → because below y=18 is hole → area 6*10=60
- From x=14 to 16 (2 cm): full height 28 cm? But the diagram shows the hole is only in the middle-right, and the far right might be solid.

Looking back: the label "6 cm" is under the hole, and "8 cm" under the left part, and total width 16 cm, so the right part should be 16-8-6=2 cm, and it should be full height, since no indication otherwise.

But in the diagram, the hole is shown as a rectangle cut out from the right side, but not necessarily touching the bottom or top? The label "18 cm" is the height of the hole, and it's positioned such that from the bottom, it starts at some point.

Actually, the diagram likely means that the hole is 18 cm high and is located with its bottom at the bottom of the figure? Or not?

Re-examining: the outer rectangle is 16x28. Inside, on the right, there is a rectangle cut out that is 6 cm wide and 18 cm high. The position: the label "8 cm" is on the bottom left, suggesting that from left to the start of the hole is 8 cm, and the hole is 6 cm wide, so from x=8 to x=14 is the hole, and x=14 to 16 is solid.

Now, vertically: the hole is 18 cm high. Is it from the bottom or from the top? The label "18 cm" is written vertically inside the hole, and there's no other label, so likely it's from the bottom up, or centered? But typically in such problems, if not specified, it might be from the bottom.

However, in the diagram, it might be that the hole does not touch the bottom. But there's no label for that.

Another way: the remaining part on the right of the hole is 2 cm wide, and it should be full height if the hole is only in the middle, but the problem doesn't specify.

I think I made a mistake. Let me think differently.

The shape is a large rectangle with a smaller rectangle removed from the interior on the right side.

The dimensions given:
- Overall: 16 cm wide, 28 cm high
- The removed rectangle: 6 cm wide, 18 cm high
- Its position: from the left, the distance to the left edge of the hole is 8 cm (as labeled "8 cm" under the left part), and the hole is 6 cm wide, so it occupies x=8 to x=14.
Vertically, the hole is 18 cm high. Where is it placed? The diagram doesn't specify, but often in such cases, it's assumed to be from the bottom or centered. However, looking at the context, and since there's no other label, perhaps it's from the bottom.

But if it's from the bottom, then the area above the hole on the right would be solid.

So:
- Left part: x=0 to 8, y=0 to 28 → 8*28=224
- Hole: x=8 to 14, y=0 to 18 → area 6*18=108 (removed)
- Right part: x=14 to 16, y=0 to 28 → 2*28=56
- Also, above the hole: x=8 to 14, y=18 to 28 → 6*10=60

So total area = left + right + above hole = 224 + 56 + 60 = 340 sq cm

Same as before: outer 16*28=448 minus hole 108 = 340.

And the above-hole part is included in the calculation.

So yes, 340 sq cm

If the hole were not from the bottom, we'd need more info, but here it works.

✔ 340 sq cm

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Now, compiling all answers:

1. 475 sq ft
2. 700 sq cm
3. 604 sq m
4. 120 sq ft
5. 256 sq yd
6. 312 sq m
7. 36 sq mm
8. 340 sq cm

Final Answer:
1. 475
2. 700
3. 604
4. 120
5. 256
6. 312
7. 36
8. 340