Let's solve each problem step by step, using the method of
splitting quadrilaterals into rectangles and triangles to find their areas.
---
🔷 Problem 1: Trapezoid
- Top base = 6 in
- Bottom base = 8 in
- Height = 5 in
This is a
trapezoid, so we can use the formula:
$$
\text{Area} = \frac{1}{2} \times (b_1 + b_2) \times h
$$
$$
= \frac{1}{2} \times (6 + 8) \times 5 = \frac{1}{2} \times 14 \times 5 = 35 \text{ in}^2
$$
✔ Area = 35 in²
---
🔷 Problem 2: Parallelogram
- Base = 27 m
- Height = 9 m
We can split this into a rectangle and two right triangles (or just use the parallelogram formula):
$$
\text{Area} = \text{base} \times \text{height} = 27 \times 9 = 243 \text{ m}^2
$$
✔ Area = 243 m²
---
🔷 Problem 3: Kite or Rhombus?
It looks like a
kite with diagonals:
- One diagonal = 10 cm (horizontal)
- Other diagonal = 4 cm (vertical)
A kite’s area is:
$$
\text{Area} = \frac{1}{2} \times d_1 \times d_2 = \frac{1}{2} \times 10 \times 4 = 20 \text{ cm}^2
$$
Alternatively, you can split it into two triangles:
- Each triangle has base 10 cm and height 2 cm (half of 4 cm), but since both are identical:
$$
\text{Area} = 2 \times \left(\frac{1}{2} \times 10 \times 2\right) = 2 \times 10 = 20 \text{ cm}^2
$$
✔ Area = 20 cm²
---
🔷 Problem 4: Trapezoid
- Top base = 13 cm
- Bottom base = 11 cm
- Height = 3 cm
Use trapezoid formula:
$$
\text{Area} = \frac{1}{2} \times (13 + 11) \times 3 = \frac{1}{2} \times 24 \times 3 = 36 \text{ cm}^2
$$
✔ Area = 36 cm²
---
🔷 Problem 5: Parallelogram
- Base = 15 ft
- Height = 7 ft
$$
\text{Area} = 15 \times 7 = 105 \text{ ft}^2
$$
✔ Area = 105 ft²
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🔷 Problem 6: Rectangle
- Length = 7 cm
- Width = 4 cm
$$
\text{Area} = 7 \times 4 = 28 \text{ cm}^2
$$
✔ Area = 28 cm²
---
🔷 Problem 7: Square
- Side = 3.5 in
$$
\text{Area} = 3.5 \times 3.5 = 12.25 \text{ in}^2
$$
✔ Area = 12.25 in²
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🔷 Problem 8: Rhombus or Diamond Shape
This is a rhombus split into two triangles by a vertical line of length 4 cm, and horizontal diagonal 12 cm.
The diagonals are:
- Horizontal diagonal = 12 cm
- Vertical diagonal = 4 cm
So, area of a rhombus:
$$
\text{Area} = \frac{1}{2} \times d_1 \times d_2 = \frac{1}{2} \times 12 \times 4 = 24 \text{ cm}^2
$$
Alternatively, split into two congruent triangles:
Each triangle has base 12 cm and height 2 cm (since 4 cm is total height, split in half).
$$
\text{Area of one triangle} = \frac{1}{2} \times 12 \times 2 = 12
$$
$$
\text{Total area} = 2 \times 12 = 24 \text{ cm}^2
$$
✔ Area = 24 cm²
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✔ Final Answers:
| Problem | Area |
|--------|------|
| 1 |
35 in² |
| 2 |
243 m² |
| 3 |
20 cm² |
| 4 |
36 cm² |
| 5 |
105 ft² |
| 6 |
28 cm² |
| 7 |
12.25 in² |
| 8 |
24 cm² |
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Let me know if you'd like these explained visually or drawn out!
Parent Tip: Review the logic above to help your child master the concept of special quadrilaterals worksheet.
