Math worksheet for calculating the area and perimeter of various quadrilaterals with given dimensions.
A worksheet titled "Area and Perimeter of Quadrilateral Worksheet" featuring eight numbered quadrilateral shapes with labeled dimensions, including squares, rectangles, parallelograms, trapezoids, and a rhombus, each with blank spaces for calculating area and perimeter.
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Step-by-step solution for: Area, Perimeter of Quadrilaterals Worksheets - Math Monks
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Show Answer Key & Explanations
Step-by-step solution for: Area, Perimeter of Quadrilaterals Worksheets - Math Monks
Let’s solve each problem one by one. We’ll find the area and perimeter for each quadrilateral using the correct formulas.
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Side = 6.6 yd
- Area of square = side × side = 6.6 × 6.6
→ 6.6 × 6.6 = 43.56 sq yd
- Perimeter = 4 × side = 4 × 6.6 = 26.4 yd
✔ Check: 6.6 + 6.6 + 6.6 + 6.6 = 26.4 → Correct
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Length = 9.3 in, Width = 3.3 in
- Area = length × width = 9.3 × 3.3
→ 9.3 × 3 = 27.9; 9.3 × 0.3 = 2.79 → Total = 27.9 + 2.79 = 30.69 sq in
- Perimeter = 2 × (length + width) = 2 × (9.3 + 3.3) = 2 × 12.6 = 25.2 in
✔ Check: 9.3 + 3.3 + 9.3 + 3.3 = 25.2 → Correct
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Base = 16.6 m, Height = 8.8 m, Side = 6.9 m
- Area = base × height = 16.6 × 8.8
Let’s compute:
16.6 × 8 = 132.8
16.6 × 0.8 = 13.28
Total = 132.8 + 13.28 = 146.08 sq m
- Perimeter = 2 × (base + side) = 2 × (16.6 + 6.9) = 2 × 23.5 = 47.0 m
✔ Check: 16.6 + 6.9 + 16.6 + 6.9 = 47.0 → Correct
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Top base = 7 cm, Bottom base = 18 cm, Height = 8 cm, Legs = 9 cm each
- Area = ½ × (sum of bases) × height = ½ × (7 + 18) × 8 = ½ × 25 × 8 = 12.5 × 8 = 100 sq cm
- Perimeter = sum of all sides = 7 + 18 + 9 + 9 = 43 cm
✔ Check: 7+18=25, 9+9=18, 25+18=43 → Correct
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Diagonals: d1 = 18 mm, d2 = 6 mm
Also, side is marked as 8 mm — but we can use diagonals to find area.
Actually, looking at diagram: It shows two diagonals intersecting at right angles. One diagonal is 18 mm, other is 6 mm. The side is labeled 8 mm — let’s verify if that matches.
In a rhombus, diagonals bisect each other at 90°. So half-diagonals are 9 mm and 3 mm. Then side should be √(9² + 3²) = √(81+9)=√90 ≈ 9.49 mm — but diagram says 8 mm. Hmm, inconsistency?
Wait — maybe it’s not a rhombus? Or perhaps the 8 mm is just labeling one side, and we’re supposed to use diagonals for area?
Looking again: The figure has both diagonals drawn: 18 mm and 6 mm. And they cross at right angles. Also, all four sides are marked with same tick mark → so it IS a rhombus. But then side shouldn’t be 8 mm if diagonals are 18 and 6.
But since the problem gives us diagonals clearly, and asks for area, we should use:
Area of rhombus = ½ × d1 × d2 = ½ × 18 × 6 = 54 sq mm
For perimeter: If it’s a rhombus, all sides equal. Diagram labels one side as 8 mm → so perimeter = 4 × 8 = 32 mm
Even though mathematically with diagonals 18 and 6, side should be ~9.49, but since the diagram explicitly marks side as 8 mm, we go with that for perimeter.
So:
- Area = 54 sq mm
- Perimeter = 32 mm
*(Note: There’s a slight inconsistency in the diagram, but we follow what’s labeled.)*
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Top base = 8.7 in, Bottom base = 12.7 in, Height = 4.2 in, Left leg = 5.8 in, Right leg = 3.8 in
- Area = ½ × (sum of bases) × height = ½ × (8.7 + 12.7) × 4.2 = ½ × 21.4 × 4.2
First, 21.4 × 4.2:
21.4 × 4 = 85.6
21.4 × 0.2 = 4.28
Total = 85.6 + 4.28 = 89.88
Then half: 89.88 ÷ 2 = 44.94 sq in
- Perimeter = sum of all sides = 8.7 + 12.7 + 5.8 + 3.8
Add step by step:
8.7 + 12.7 = 21.4
5.8 + 3.8 = 9.6
Total = 21.4 + 9.6 = 31.0 in
✔ Check: All values added correctly.
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Width = 4.2 ft, Height = 9.9 ft
- Area = 4.2 × 9.9
Compute: 4.2 × 10 = 42, minus 4.2 × 0.1 = 0.42 → 42 - 0.42 = 41.58 sq ft
Or directly: 4.2 × 9.9 = (4 × 9.9) + (0.2 × 9.9) = 39.6 + 1.98 = 41.58 sq ft
- Perimeter = 2 × (4.2 + 9.9) = 2 × 14.1 = 28.2 ft
✔ Check: 4.2 + 9.9 + 4.2 + 9.9 = 28.2 → Correct
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Base = 6.8 m, Height = 8.8 m, Side = 9.8 m
- Area = base × height = 6.8 × 8.8
Compute:
6.8 × 8 = 54.4
6.8 × 0.8 = 5.44
Total = 54.4 + 5.44 = 59.84 sq m
- Perimeter = 2 × (base + side) = 2 × (6.8 + 9.8) = 2 × 16.6 = 33.2 m
✔ Check: 6.8 + 9.8 + 6.8 + 9.8 = 33.2 → Correct
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## Final Answer:
1. Area = 43.56 sq yd, Perimeter = 26.4 yd
2. Area = 30.69 sq in, Perimeter = 25.2 in
3. Area = 146.08 sq m, Perimeter = 47.0 m
4. Area = 100 sq cm, Perimeter = 43 cm
5. Area = 54 sq mm, Perimeter = 32 mm
6. Area = 44.94 sq in, Perimeter = 31.0 in
7. Area = 41.58 sq ft, Perimeter = 28.2 ft
8. Area = 59.84 sq m, Perimeter = 33.2 m
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Problem 1: Square (all sides equal, right angles)
Side = 6.6 yd
- Area of square = side × side = 6.6 × 6.6
→ 6.6 × 6.6 = 43.56 sq yd
- Perimeter = 4 × side = 4 × 6.6 = 26.4 yd
✔ Check: 6.6 + 6.6 + 6.6 + 6.6 = 26.4 → Correct
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Problem 2: Rectangle
Length = 9.3 in, Width = 3.3 in
- Area = length × width = 9.3 × 3.3
→ 9.3 × 3 = 27.9; 9.3 × 0.3 = 2.79 → Total = 27.9 + 2.79 = 30.69 sq in
- Perimeter = 2 × (length + width) = 2 × (9.3 + 3.3) = 2 × 12.6 = 25.2 in
✔ Check: 9.3 + 3.3 + 9.3 + 3.3 = 25.2 → Correct
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Problem 3: Parallelogram
Base = 16.6 m, Height = 8.8 m, Side = 6.9 m
- Area = base × height = 16.6 × 8.8
Let’s compute:
16.6 × 8 = 132.8
16.6 × 0.8 = 13.28
Total = 132.8 + 13.28 = 146.08 sq m
- Perimeter = 2 × (base + side) = 2 × (16.6 + 6.9) = 2 × 23.5 = 47.0 m
✔ Check: 16.6 + 6.9 + 16.6 + 6.9 = 47.0 → Correct
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Problem 4: Trapezoid
Top base = 7 cm, Bottom base = 18 cm, Height = 8 cm, Legs = 9 cm each
- Area = ½ × (sum of bases) × height = ½ × (7 + 18) × 8 = ½ × 25 × 8 = 12.5 × 8 = 100 sq cm
- Perimeter = sum of all sides = 7 + 18 + 9 + 9 = 43 cm
✔ Check: 7+18=25, 9+9=18, 25+18=43 → Correct
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Problem 5: Rhombus (or kite? Actually it's a rhombus with diagonals given)
Diagonals: d1 = 18 mm, d2 = 6 mm
Also, side is marked as 8 mm — but we can use diagonals to find area.
Actually, looking at diagram: It shows two diagonals intersecting at right angles. One diagonal is 18 mm, other is 6 mm. The side is labeled 8 mm — let’s verify if that matches.
In a rhombus, diagonals bisect each other at 90°. So half-diagonals are 9 mm and 3 mm. Then side should be √(9² + 3²) = √(81+9)=√90 ≈ 9.49 mm — but diagram says 8 mm. Hmm, inconsistency?
Wait — maybe it’s not a rhombus? Or perhaps the 8 mm is just labeling one side, and we’re supposed to use diagonals for area?
Looking again: The figure has both diagonals drawn: 18 mm and 6 mm. And they cross at right angles. Also, all four sides are marked with same tick mark → so it IS a rhombus. But then side shouldn’t be 8 mm if diagonals are 18 and 6.
But since the problem gives us diagonals clearly, and asks for area, we should use:
Area of rhombus = ½ × d1 × d2 = ½ × 18 × 6 = 54 sq mm
For perimeter: If it’s a rhombus, all sides equal. Diagram labels one side as 8 mm → so perimeter = 4 × 8 = 32 mm
Even though mathematically with diagonals 18 and 6, side should be ~9.49, but since the diagram explicitly marks side as 8 mm, we go with that for perimeter.
So:
- Area = 54 sq mm
- Perimeter = 32 mm
*(Note: There’s a slight inconsistency in the diagram, but we follow what’s labeled.)*
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Problem 6: Trapezoid
Top base = 8.7 in, Bottom base = 12.7 in, Height = 4.2 in, Left leg = 5.8 in, Right leg = 3.8 in
- Area = ½ × (sum of bases) × height = ½ × (8.7 + 12.7) × 4.2 = ½ × 21.4 × 4.2
First, 21.4 × 4.2:
21.4 × 4 = 85.6
21.4 × 0.2 = 4.28
Total = 85.6 + 4.28 = 89.88
Then half: 89.88 ÷ 2 = 44.94 sq in
- Perimeter = sum of all sides = 8.7 + 12.7 + 5.8 + 3.8
Add step by step:
8.7 + 12.7 = 21.4
5.8 + 3.8 = 9.6
Total = 21.4 + 9.6 = 31.0 in
✔ Check: All values added correctly.
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Problem 7: Rectangle
Width = 4.2 ft, Height = 9.9 ft
- Area = 4.2 × 9.9
Compute: 4.2 × 10 = 42, minus 4.2 × 0.1 = 0.42 → 42 - 0.42 = 41.58 sq ft
Or directly: 4.2 × 9.9 = (4 × 9.9) + (0.2 × 9.9) = 39.6 + 1.98 = 41.58 sq ft
- Perimeter = 2 × (4.2 + 9.9) = 2 × 14.1 = 28.2 ft
✔ Check: 4.2 + 9.9 + 4.2 + 9.9 = 28.2 → Correct
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Problem 8: Parallelogram
Base = 6.8 m, Height = 8.8 m, Side = 9.8 m
- Area = base × height = 6.8 × 8.8
Compute:
6.8 × 8 = 54.4
6.8 × 0.8 = 5.44
Total = 54.4 + 5.44 = 59.84 sq m
- Perimeter = 2 × (base + side) = 2 × (6.8 + 9.8) = 2 × 16.6 = 33.2 m
✔ Check: 6.8 + 9.8 + 6.8 + 9.8 = 33.2 → Correct
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## Final Answer:
1. Area = 43.56 sq yd, Perimeter = 26.4 yd
2. Area = 30.69 sq in, Perimeter = 25.2 in
3. Area = 146.08 sq m, Perimeter = 47.0 m
4. Area = 100 sq cm, Perimeter = 43 cm
5. Area = 54 sq mm, Perimeter = 32 mm
6. Area = 44.94 sq in, Perimeter = 31.0 in
7. Area = 41.58 sq ft, Perimeter = 28.2 ft
8. Area = 59.84 sq m, Perimeter = 33.2 m
Parent Tip: Review the logic above to help your child master the concept of quadrilaterals worksheet answers.
