Let's solve each of these quadrilateral area problems step by step, using the hints provided and splitting the shapes into simpler parts (rectangles and triangles) where needed.
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1) Trapezium
- Top base = 12 cm
- Bottom base = 10 cm
- Height = 4 cm
This is a
trapezium. Use the formula:
> Area = ½ × (base₁ + base₂) × height
> = ½ × (12 + 10) × 4
> = ½ × 22 × 4
> = 11 × 4 =
44 cm²
✔ Area = 44 cm²
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2) Trapezium
- Top base = 10 m
- Bottom base = 6 m
- Height = 5 m
Again, use the trapezium formula:
> Area = ½ × (10 + 6) × 5
> = ½ × 16 × 5
> = 8 × 5 =
40 m²
✔ Area = 40 m²
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3) Parallelogram
- Base = 11 mm
- Height = 7 mm
Use the parallelogram formula:
> Area = base × height
> = 11 × 7 =
77 mm²
✔ Area = 77 mm²
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4) Rhombus (or kite-like shape)
- Diagonals: one diagonal is 9 m, the other is 3 m
This is a
rhombus or a kite, and we can split it into two congruent triangles along the diagonals.
But there's a shortcut:
> Area of a rhombus = ½ × d₁ × d₂
> = ½ × 9 × 3
> = ½ × 27 =
13.5 m²
Alternatively, split into two triangles:
- Each triangle has base = 9 m, height = 1.5 m (half of 3 m)
- But better to use the formula.
✔ Area = 13.5 m²
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5) Rhombus
- Diagonals: 11 cm and 5 cm
Same as above:
> Area = ½ × d₁ × d₂
> = ½ × 11 × 5
> = ½ × 55 =
27.5 cm²
✔ Area = 27.5 cm²
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6) Parallelogram
- Base = 30 mm
- Height = 9 mm
Use the parallelogram formula:
> Area = base × height
> = 30 × 9 =
270 mm²
✔ Area = 270 mm²
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✔ Final Answers:
1)
44 cm²
2)
40 m²
3)
77 mm²
4)
13.5 m²
5)
27.5 cm²
6)
270 mm²
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🔍 Explanation Summary:
-
Trapeziums (problems 1 & 2): Use the average of the two parallel sides times height.
-
Parallelograms (problems 3 & 6): Use base × perpendicular height.
-
Rhombuses/kites (problems 4 & 5): Use ½ × d₁ × d₂ (product of diagonals divided by 2).
Even though the instruction says "split into rectangles and triangles", for most of these, direct formulas are efficient and accurate. However, if you wanted to split them up:
- For
parallelograms, you could cut off a triangle from one side and move it to the other to form a rectangle.
- For
trapeziums, you could split into a rectangle and two right triangles.
- For
rhombuses, they naturally split into four right triangles or two pairs of congruent triangles via diagonals.
But since the formulas are given and reliable, we used them directly.
Let me know if you'd like visual breakdowns of how to split any of them!
Parent Tip: Review the logic above to help your child master the concept of special quadrilaterals worksheet.
