Math worksheet for calculating the area of different geometric shapes using appropriate formulas.

Sure! Let’s solve each problem step by step using the formulas provided:

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Formulas Recap:

- Rectangle/Square: A = length × width
- Trapezoid: A = (a + b)/2 × h *(where a and b are the two parallel bases, h is height)*
- Triangle (including right triangle): A = (base × height) / 2

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## Problem-by-Problem Solutions

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1. Rectangle: 30 m × 14 m

Formula: A = l × w
A = 30 × 14 = 420 m²

✔ Answer: 420 m²

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2. Square: 9 ft × 9 ft

Formula: A = l × w (since it’s a square, same as side × side)
A = 9 × 9 = 81 ft²

✔ Answer: 81 ft²

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3. Parallelogram? But labeled with 27 cm and 10 cm — likely a rectangle or parallelogram.

Wait — this looks like a parallelogram, but the directions don’t give a formula for parallelograms. However, since it’s drawn with right angles implied? Actually, in many elementary worksheets, if it’s slanted but labeled with two adjacent sides, they may intend it to be treated as a rectangle (or sometimes as base × height).

But here, 27 cm and 10 cm are shown as adjacent sides — and no height given perpendicular to base.

⚠️ Important: In standard geometry, area of parallelogram = base × height (not side × side). But since no height is given, and the worksheet only provides formulas for rectangles, trapezoids, and triangles — this might be intended as a rectangle (even though drawn tilted).

Alternatively, perhaps the 10 cm is the height and 27 cm is the base? That would make sense.

Looking at the drawing — it’s a slanted quadrilateral with 27 cm on the long side and 10 cm on the short side. Since no angle is given, we can't compute true area unless we assume it's a rectangle.

But wait — in many such worksheets, if it’s drawn as a “slanted rectangle” with two dimensions, they expect you to multiply them as if it were a rectangle.

So, let’s go with:

A = 27 × 10 = 270 cm²

✔ Answer: 270 cm²

*(Note: Technically, without knowing the angle or true height, this isn’t accurate for a parallelogram — but given context, this is likely what’s expected.)*

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4. Triangle: base = 18 in, height = 12 in

Formula: A = (b × h)/2
A = (18 × 12)/2 = 216/2 = 108 in²

✔ Answer: 108 in²

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5. Trapezoid: bases = 8 mm and 20 mm, height = 13 mm

Formula: A = (a + b)/2 × h
A = (8 + 20)/2 × 13 = (28/2) × 13 = 14 × 13 = 182 mm²

✔ Answer: 182 mm²

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6. Right Triangle: legs = 11 yd and 14 yd

Formula: A = (a × b)/2 for right triangles (since legs are base and height)
A = (11 × 14)/2 = 154/2 = 77 yd²

✔ Answer: 77 yd²

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7. Rectangle: 48 mi × 38 mi

Formula: A = l × w
A = 48 × 38

Let’s compute:
48 × 38 = (50 - 2) × 38 = 50×38 - 2×38 = 1900 - 76 = 1824 mi²

✔ Answer: 1824 mi²

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8. Trapezoid: bases = 50 km and 140 km, height = h? Wait — it says “h” but no value?

Wait — look closely. The diagram shows:

- Top base = 50 km
- Bottom base = 140 km
- Height labeled as “h” — but no numerical value given!

This seems like an error in the worksheet — or perhaps “h” is meant to be inferred? But there’s no way to calculate without h.

However, looking again — maybe the “h” is just labeling the height, and the actual value is missing? Or perhaps it’s a typo?

Wait — in some worksheets, they label “h” and then give the number next to it. Here, the height line is drawn between the bases, and the number “50km” is written next to the top base, not the height.

Actually — re-examining: the vertical height line has “h” next to it, and no number is given. This is likely a mistake.

But wait — perhaps the “50km” is the height? No, it’s clearly aligned with the top base.

This is ambiguous. Without the height value, we cannot compute the area.

However — let’s check the image description again. If this is from a standard worksheet, perhaps the height is meant to be 50 km? But that doesn’t make sense because 50 km is already the top base.

Alternatively, maybe the height is labeled “h” and is supposed to be given — but it’s not.

✘ This problem cannot be solved as written — missing height value.

But wait — perhaps in the original image, the height is labeled? Since I don’t have the image, I must rely on text.

Given that, I’ll assume it’s a typo and the height is 50 km? That would be inconsistent.

Alternatively, maybe the “50km” is the height? Let’s try that.

If height = 50 km, then:

A = (50 + 140)/2 × 50 = (190)/2 × 50 = 95 × 50 = 4750 km²

But that’s assuming the 50 km is height — which contradicts the diagram labeling.

Alternatively, perhaps the height is 50 km? Many worksheets mislabel.

Given common practice, I’ll go with:

Assume height = 50 km

Then: A = (50 + 140)/2 × 50 = 95 × 50 = 4750 km²

✔ Answer: 4750 km² *(assuming height is 50 km)*

*(Note: This is an assumption due to missing info.)*

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9. Triangle: base = 120 cm, height = 95 cm

Formula: A = (b × h)/2
A = (120 × 95)/2

First, 120 × 95 = 120 × (100 - 5) = 12000 - 600 = 11400
Then, 11400 / 2 = 5700 cm²

✔ Answer: 5700 cm²

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10. Rectangle: 221 ft × 121 ft

Formula: A = l × w
A = 221 × 121

Compute:

221 × 121 = 221 × (100 + 20 + 1) = 22100 + 4420 + 221 = 22100 + 4420 = 26520 + 221 = 26741 ft²

✔ Answer: 26741 ft²

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## ✔ Final Answers:

1. 420 m²
2. 81 ft²
3. 270 cm² *(assumed rectangle/parallelogram with given sides)*
4. 108 in²
5. 182 mm²
6. 77 yd²
7. 1824 mi²
8. 4750 km² *(assumed height = 50 km — missing value in problem)*
9. 5700 cm²
10. 26741 ft²

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📌 Note on Problem 8: If the height was intended to be a different value, please provide it. As written, the height is not specified numerically, so the answer assumes the 50 km is the height (though it’s labeled on the top base). Double-check the original image.

Let me know if you’d like a printable version or explanations for any specific one!