This worksheet helps students practice calculating the area of complex shapes by breaking them down into simpler rectangles and triangles.

Let’s solve each problem one by one. We’ll break each composite figure into simpler shapes (like rectangles and triangles), find their areas, then add them up.

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Problem 1:

Figure is made of two rectangles:
- Bottom rectangle: width = 8 in, height = 4 in → Area = 8 × 4 = 32 in²
- Top rectangle: width = 4 in, height = 5 in → Area = 4 × 5 = 20 in²
Total area = 32 + 20 = 52 in²

Wait — let me double-check the diagram description. The total height on left is 9 in? Wait, no — looking again:

Actually, from the labels:
Left side says “9 in” total height? But bottom part is 4 in, top part must be 5 in? And widths: bottom is 8 in, top is 4 in? Yes.

But wait — if bottom is 8 in wide and 4 in tall, and top is centered? Or aligned to left? Doesn’t matter for area — we just add the two rectangles.

So yes: 8×4 = 32; 4×5 = 20 → Total = 52 in²

✔ Correct.

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Problem 2:

This is a triangle on top of a rectangle.

Rectangle: base = 6 ft, height = 7 ft → Area = 6 × 7 = 42 ft²
Triangle: base = 6 ft, height = 5 ft → Area = (1/2) × 6 × 5 = 15 ft²
Total = 42 + 15 = 57 ft²

✔ Correct.

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Problem 3:

L-shaped figure. Can split into two rectangles.

Option 1: Vertical rectangle on left: 5 m wide × 9 m tall = 45 m²
Horizontal rectangle on right: 12 m long × 4 m tall = 48 m²
But wait — they overlap? No, actually, if you look at it, the vertical part is 5m x 9m, and the horizontal part extends to the right from the bottom, but only 4m high. So the overlapping part is already included? Actually, better to split differently.

Better way: Split into top rectangle and bottom rectangle.

Top: width = 5 m, height = 5 m (since total height 9m, bottom part is 4m, so top is 5m) → 5×5=25
Bottom: width = 5+12=17 m? Wait no — the bottom part is only under the right extension? Let me think.

Actually, standard way: The full shape can be seen as:

- Left column: 5 m wide × 9 m tall = 45 m²
- Right extension: 12 m long × 4 m tall = 48 m²
But the corner where they meet is counted twice? No — because the right extension starts at the bottom, and the left column goes all the way up. So actually, the right extension is attached to the bottom right of the left column. So total area = 45 + 48 = 93? But that would mean the bottom right corner is added extra? Wait no — the left column is 5x9, which includes the bottom 5x4 part. Then the right extension is 12x4, which is adjacent to the right of the bottom 5x4 part. So no overlap.

Wait — but the total width at bottom is 5 + 12 = 17 m? And height 4 m for bottom, and above that only 5 m wide for 5 m height.

So area = (bottom rectangle: 17 m × 4 m) + (top rectangle: 5 m × 5 m) = 68 + 25 = 93 m²

Yes! That’s better.

Bottom: 17 × 4 = 68
Top: 5 × 5 = 25
Total = 93 m²

✔ Correct.

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Problem 4:

Trapezoid? Or can split into rectangle and triangle.

Actually, it's a trapezoid with parallel sides 10 cm and 15 cm, height 12 cm? Wait, no — the figure has left side 15 cm, right side 10 cm, bottom 12 cm, and slanted top.

Actually, it’s a trapezoid. Area of trapezoid = (a+b)/2 × h

Here, parallel sides are the two vertical sides? No — usually bases are horizontal.

Looking: left side 15 cm (vertical), right side 10 cm (vertical), bottom 12 cm (horizontal). So it’s a trapezoid with parallel sides being the left and right? No, those are not parallel unless it’s rotated.

Actually, this is a right trapezoid. The two parallel sides are the top and bottom? But top is slanted.

Wait — better to split into rectangle and triangle.

Imagine: from the right end, draw a vertical line up to the top. Since right side is 10 cm, and left is 15 cm, the difference is 5 cm. So we have a rectangle 12 cm wide × 10 cm tall, and a triangle on top with base 12 cm and height 5 cm.

Area rectangle = 12 × 10 = 120 cm²
Area triangle = (1/2) × 12 × 5 = 30 cm²
Total = 150 cm²

Alternatively, trapezoid formula: average of parallel sides times height. Here, the two parallel sides are the left and right? No — in a trapezoid, the parallel sides are the ones that are parallel. In this case, the top and bottom are not both horizontal? Actually, in the diagram, the bottom is horizontal, and the top is slanted, but the left and right are vertical? If left and right are both vertical, then they are parallel.

Oh! I think I misread. If left side is 15 cm vertical, right side is 10 cm vertical, and bottom is 12 cm horizontal, then the top is slanted. But since left and right are both vertical, they are parallel. So it’s a trapezoid with parallel sides of length 15 cm and 10 cm, and the distance between them (the height) is 12 cm.

Area = (15 + 10)/2 × 12 = 25/2 × 12 = 12.5 × 12 = 150 cm²

Same answer.

✔ Correct.

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Problem 5:

Pentagon-like shape. Can split into rectangle and triangle.

Rectangle: 16 mm × 8 mm = 128 mm²
Triangle on right: base = ? The total length is 21 mm, rectangle is 16 mm, so triangle base = 21 - 16 = 5 mm. Height of triangle is same as rectangle height? From diagram, the triangle is on the right, and its height should be the same as the rectangle’s height, which is 8 mm? But wait, the label says "8 mm" on the left side, and the triangle is attached to the right.

Actually, looking: the figure has a rectangle 16 mm long and 8 mm high, and then a triangle attached to the right side. The triangle has base along the right edge? Or extending out?

The total length is 21 mm, so the triangle extends 5 mm beyond the rectangle. And the height of the triangle — since it’s symmetric? The diagram shows the triangle pointing right, and the height should be the same as the rectangle’s height, 8 mm? But in a triangle, if it’s attached to the side, the base might be vertical.

Wait — actually, in such problems, when a triangle is attached to the end of a rectangle like this, it’s usually an isosceles triangle with base equal to the height of the rectangle.

Standard interpretation: the triangle has base = 8 mm (same as rectangle height), and height = 5 mm (since 21 - 16 = 5).

Is that correct? Let me see: if the rectangle is 16 mm long and 8 mm high, and we attach a triangle to the right end, making the total length 21 mm, then the triangle must extend 5 mm to the right. For the triangle to fit, its base should be the same as the rectangle’s height, 8 mm, and its height (altitude) is 5 mm.

Area of triangle = (1/2) × base × height = (1/2) × 8 × 5 = 20 mm²
Area of rectangle = 16 × 8 = 128 mm²
Total = 128 + 20 = 148 mm²

But is the base of the triangle 8 mm? Yes, because it’s attached to the 8 mm side of the rectangle.

✔ Correct.

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Problem 6:

Another L-shape or T-shape? Looks like a cross or something.

From diagram: it’s like a plus sign but missing parts? Actually, it’s composed of three rectangles.

We can split it as:

- Middle vertical rectangle: width 3 yd, height 14 yd? But there are extensions.

Better: think of it as a large rectangle minus cutouts, but easier to add parts.

Notice: the figure has a central part.

Split into:

- Bottom rectangle: 10 yd wide × 3 yd high = 30 yd²
- Middle rectangle: 3 yd wide × (14 - 3 - 3) = 3 × 8 = 24 yd²? Wait, total height is 14 yd, bottom is 3 yd, top is 3 yd, so middle is 8 yd. But the middle part is only 3 yd wide? And the top and bottom are wider.

Actually, the top part is 3 yd high and 10 yd wide? Same as bottom.

And the middle part connects them, but is narrower.

So:

- Top rectangle: 10 yd × 3 yd = 30 yd²
- Bottom rectangle: 10 yd × 3 yd = 30 yd²
- Middle rectangle: 3 yd × (14 - 3 - 3) = 3 × 8 = 24 yd²
Total = 30 + 30 + 24 = 84 yd²

But is the middle part really 3 yd wide? Yes, from the diagram, the arms are 3 yd thick.

Also, check: total height 14 yd, with top and bottom each 3 yd, so middle section height is 8 yd, width 3 yd.

Yes.

Alternative: imagine the whole thing as a big rectangle 10 yd × 14 yd = 140 yd², minus the two side cutouts.

Each cutout is a rectangle: width = (10 - 3)/2 = 3.5 yd? No, because the middle is 3 yd, so each side has (10 - 3)/2 = 3.5 yd, and height of cutout is 8 yd (since top and bottom are full).

So each cutout: 3.5 × 8 = 28 yd², two of them: 56 yd²
Total area = 140 - 56 = 84 yd²

Same answer.

✔ Correct.

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Problem 7:

Similar to problem 1.

Two rectangles:

- Bottom: 10 yd × 3 yd = 30 yd²
- Top: 4 yd × 6 yd = 24 yd²
Total = 30 + 24 = 54 yd²

Check heights: total height on left is 9 yd? Bottom 3 yd, top 6 yd, yes. Widths: bottom 10 yd, top 4 yd.

Yes.

✔ Correct.

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Problem 8:

Rectangle with a smaller rectangle on top? Or is it a single shape?

From diagram: it looks like a rectangle 10 ft wide and 6 ft high, but with a protrusion on top? Actually, it says "composite figure", and labels: bottom part 10 ft wide, 6 ft high? But then on top, there’s a part that is 4 ft wide and 3 ft high? But how is it attached?

Looking: the total height is not given, but from the labels, the bottom rectangle is 10 ft × 6 ft, and on top of it, centered or something, a smaller rectangle 4 ft × 3 ft.

But if it’s on top, then total area = area of bottom + area of top = 10×6 + 4×3 = 60 + 12 = 72 ft²

Is that correct? The diagram might show that the top part is sitting on the bottom, so yes.

But let me confirm: sometimes it might be indented, but here it seems added on top.

Yes.

✔ Correct.

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Problem 9:

Another L-shape.

Can split into two rectangles.

Option: vertical part: 6 ft wide × 9 ft high = 54 ft²
Horizontal part: 8 ft long × 4 ft high = 32 ft²
But they overlap in the corner? The overlapping region is 6 ft × 4 ft? No.

Actually, if the vertical part is 6 ft wide and 9 ft high, and the horizontal part extends to the right from the bottom, 8 ft long and 4 ft high, then the overlapping part is the bottom-left 6 ft × 4 ft, which is already included in the vertical rectangle.

So if I add 54 + 32, I’m double-counting the 6×4=24 ft².

So total area = 54 + 32 - 24 = 62 ft²

Better way: split without overlap.

Split into:

- Left rectangle: 6 ft × 9 ft = 54 ft²
- Right rectangle: (8 - 6) ft × 4 ft = 2 ft × 4 ft = 8 ft²
Total = 54 + 8 = 62 ft²

Yes.

Or: bottom rectangle: 8 ft × 4 ft = 32 ft²
Top rectangle: 6 ft × (9 - 4) = 6 × 5 = 30 ft²
Total = 32 + 30 = 62 ft²

Same.

✔ Correct.

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Now, compiling all answers:

1. 52 in²
2. 57 ft²
3. 93 m²
4. 150 cm²
5. 148 mm²
6. 84 yd²
7. 54 yd²
8. 72 ft²
9. 62 ft²

I think that’s all.

Final Answer:
1. 52
2. 57
3. 93
4. 150
5. 148
6. 84
7. 54
8. 72
9. 62