Finding the Area of Quadrilaterals worksheet - Free Printable
Educational worksheet: Finding the Area of Quadrilaterals worksheet. Download and print for classroom or home learning activities.
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Step-by-step solution for: Finding the Area of Quadrilaterals worksheet
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Show Answer Key & Explanations
Step-by-step solution for: Finding the Area of Quadrilaterals worksheet
Let’s solve each problem one by one. We’ll use the correct area formula for each shape.
---
1. Square with side 4 cm
Area of square = side × side
= 4 cm × 4 cm = 16 cm²
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2. Square with side 12 mm
Area = 12 mm × 12 mm = 144 mm²
---
3. Rectangle: length 11 cm, width 6 cm
Area = length × width
= 11 cm × 6 cm = 66 cm²
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4. Parallelogram: base 12 m, height 3 m
Area = base × height
= 12 m × 3 m = 36 m²
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5. Rectangle: length 7 ft, width 9 ft
Area = 7 ft × 9 ft = 63 ft²
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6. Trapezoid: bases 8 cm and 14 cm, height 6 cm
Area = (base1 + base2) ÷ 2 × height
= (8 + 14) ÷ 2 × 6
= 22 ÷ 2 × 6
= 11 × 6 = 66 cm²
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7. Rectangle: length 7 mm, width 5 mm
Area = 7 mm × 5 mm = 35 mm²
---
8. Square with side 9 m
Area = 9 m × 9 m = 81 m²
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9. Parallelogram: base 18 cm, height 10 mm → WAIT! Units are different!
We must convert to same units. Let’s convert everything to cm.
Height = 10 mm = 1 cm
Base = 18 cm
Area = base × height = 18 cm × 1 cm = 18 cm²
*(Note: If we kept it in mm, base would be 180 mm, height 10 mm → 180×10=1800 mm², which is same as 18 cm² — so either way works if consistent. But since answer space doesn’t specify unit, we’ll match the base unit given — cm — so 18 cm² is fine.)*
Actually, looking again — the height is labeled “10 mm” and base “18 cm”. To avoid confusion, let’s convert both to mm:
Base = 18 cm = 180 mm
Height = 10 mm
Area = 180 mm × 10 mm = 1800 mm²
But the worksheet might expect you to notice the mismatch and convert. Since other problems mix units sometimes, but here it’s likely a trick. However, in most school worksheets, they expect you to use the numbers as given without converting unless specified. Wait — that can’t be right because area would be wrong.
Actually, let me check the image again mentally — in problem 9, the height arrow says “10 mm”, and base says “18 cm”. That’s inconsistent. But in real math, you MUST convert.
So better to convert to same unit. Let’s pick cm:
10 mm = 1 cm
So area = 18 cm × 1 cm = 18 cm²
I think that’s what’s expected. Some worksheets do this to test attention to units.
Alternatively, maybe it’s a typo? But we have to go with what’s written.
I’ll go with 18 cm² after conversion.
Wait — actually, looking at problem 4: height is 3 m, base 12 m — same units. Problem 9 is the only one with mixed units. So probably intentional.
Final decision: Convert 10 mm to 1 cm → Area = 18 × 1 = 18 cm²
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10. Trapezoid: bases 27 cm and 15 cm, height 5 cm
Area = (27 + 15) ÷ 2 × 5
= 42 ÷ 2 × 5
= 21 × 5 = 105 cm²
---
Now let’s list all answers clearly:
1. 16 cm²
2. 144 mm²
3. 66 cm²
4. 36 m²
5. 63 ft²
6. 66 cm²
7. 35 mm²
8. 81 m²
9. 18 cm² *(after converting 10 mm to 1 cm)*
10. 105 cm²
Wait — for #9, if we don’t convert, and just multiply 18 cm × 10 mm, that’s not valid. You can’t multiply cm × mm directly for area without converting. So yes, conversion is necessary.
Some might argue to leave as 1800 mm², but since the base is given in cm, and no instruction, I think 18 cm² is more appropriate.
Actually, let me double-check standard practice: In such worksheets, if units differ, you convert to the smaller or larger? Usually, convert to match the base or the majority. Here, base is in cm, height in mm — convert height to cm.
Yes, 10 mm = 1 cm → 18 × 1 = 18 cm².
Okay, confident now.
---
Final Answer:
1. 16 cm²
2. 144 mm²
3. 66 cm²
4. 36 m²
5. 63 ft²
6. 66 cm²
7. 35 mm²
8. 81 m²
9. 18 cm²
10. 105 cm²
---
1. Square with side 4 cm
Area of square = side × side
= 4 cm × 4 cm = 16 cm²
---
2. Square with side 12 mm
Area = 12 mm × 12 mm = 144 mm²
---
3. Rectangle: length 11 cm, width 6 cm
Area = length × width
= 11 cm × 6 cm = 66 cm²
---
4. Parallelogram: base 12 m, height 3 m
Area = base × height
= 12 m × 3 m = 36 m²
---
5. Rectangle: length 7 ft, width 9 ft
Area = 7 ft × 9 ft = 63 ft²
---
6. Trapezoid: bases 8 cm and 14 cm, height 6 cm
Area = (base1 + base2) ÷ 2 × height
= (8 + 14) ÷ 2 × 6
= 22 ÷ 2 × 6
= 11 × 6 = 66 cm²
---
7. Rectangle: length 7 mm, width 5 mm
Area = 7 mm × 5 mm = 35 mm²
---
8. Square with side 9 m
Area = 9 m × 9 m = 81 m²
---
9. Parallelogram: base 18 cm, height 10 mm → WAIT! Units are different!
We must convert to same units. Let’s convert everything to cm.
Height = 10 mm = 1 cm
Base = 18 cm
Area = base × height = 18 cm × 1 cm = 18 cm²
*(Note: If we kept it in mm, base would be 180 mm, height 10 mm → 180×10=1800 mm², which is same as 18 cm² — so either way works if consistent. But since answer space doesn’t specify unit, we’ll match the base unit given — cm — so 18 cm² is fine.)*
Actually, looking again — the height is labeled “10 mm” and base “18 cm”. To avoid confusion, let’s convert both to mm:
Base = 18 cm = 180 mm
Height = 10 mm
Area = 180 mm × 10 mm = 1800 mm²
But the worksheet might expect you to notice the mismatch and convert. Since other problems mix units sometimes, but here it’s likely a trick. However, in most school worksheets, they expect you to use the numbers as given without converting unless specified. Wait — that can’t be right because area would be wrong.
Actually, let me check the image again mentally — in problem 9, the height arrow says “10 mm”, and base says “18 cm”. That’s inconsistent. But in real math, you MUST convert.
So better to convert to same unit. Let’s pick cm:
10 mm = 1 cm
So area = 18 cm × 1 cm = 18 cm²
I think that’s what’s expected. Some worksheets do this to test attention to units.
Alternatively, maybe it’s a typo? But we have to go with what’s written.
I’ll go with 18 cm² after conversion.
Wait — actually, looking at problem 4: height is 3 m, base 12 m — same units. Problem 9 is the only one with mixed units. So probably intentional.
Final decision: Convert 10 mm to 1 cm → Area = 18 × 1 = 18 cm²
---
10. Trapezoid: bases 27 cm and 15 cm, height 5 cm
Area = (27 + 15) ÷ 2 × 5
= 42 ÷ 2 × 5
= 21 × 5 = 105 cm²
---
Now let’s list all answers clearly:
1. 16 cm²
2. 144 mm²
3. 66 cm²
4. 36 m²
5. 63 ft²
6. 66 cm²
7. 35 mm²
8. 81 m²
9. 18 cm² *(after converting 10 mm to 1 cm)*
10. 105 cm²
Wait — for #9, if we don’t convert, and just multiply 18 cm × 10 mm, that’s not valid. You can’t multiply cm × mm directly for area without converting. So yes, conversion is necessary.
Some might argue to leave as 1800 mm², but since the base is given in cm, and no instruction, I think 18 cm² is more appropriate.
Actually, let me double-check standard practice: In such worksheets, if units differ, you convert to the smaller or larger? Usually, convert to match the base or the majority. Here, base is in cm, height in mm — convert height to cm.
Yes, 10 mm = 1 cm → 18 × 1 = 18 cm².
Okay, confident now.
---
Final Answer:
1. 16 cm²
2. 144 mm²
3. 66 cm²
4. 36 m²
5. 63 ft²
6. 66 cm²
7. 35 mm²
8. 81 m²
9. 18 cm²
10. 105 cm²
Parent Tip: Review the logic above to help your child master the concept of quadrilateral area worksheet answers.
