Free Geometry Worksheets pdf Download | Math Champions - Free Printable

Let's solve each problem step by step. We are asked to find the perimeter and area of each shape. All shapes are trapezoids, except possibly some that may be parallelograms or triangles (but based on labels, they're all trapezoids).

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🔷 Formulas Used:

- Perimeter: Sum of all side lengths.
- Area of a Trapezoid:
$$
\text{Area} = \frac{1}{2} \times (b_1 + b_2) \times h
$$
where $ b_1 $ and $ b_2 $ are the two parallel bases, and $ h $ is the height (perpendicular distance between them).

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We'll go through each one:

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1.

- Sides: 4 cm, 3.29 cm, 3.40 cm, 2 cm
- Height: 3 cm (vertical dashed line)
- Bases: top = 4 cm, bottom = 2 cm

Perimeter:
$$
P = 4 + 3.29 + 3.40 + 2 = 12.69\ \text{cm}
$$

Area:
$$
A = \frac{1}{2} \times (4 + 2) \times 3 = \frac{1}{2} \times 6 \times 3 = 9\ \text{cm}^2
$$

✔ Answer:
Perimeter = 12.69 cm, Area = 9 cm²

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2.

- Sides: 7 cm, 6.08 cm, 6.63 cm, 3 cm
- Height: 6 cm
- Bases: top = 7 cm, bottom = 3 cm

Perimeter:
$$
P = 7 + 6.08 + 6.63 + 3 = 22.71\ \text{cm}
$$

Area:
$$
A = \frac{1}{2} \times (7 + 3) \times 6 = \frac{1}{2} \times 10 \times 6 = 30\ \text{cm}^2
$$

✔ Answer:
Perimeter = 22.71 cm, Area = 30 cm²

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3.

- Sides: 11 cm, 8.88 cm, 8.81 cm, 5 cm
- Height: 8 cm
- Bases: top = 11 cm, bottom = 5 cm

Perimeter:
$$
P = 11 + 8.88 + 8.81 + 5 = 33.69\ \text{cm}
$$

Area:
$$
A = \frac{1}{2} \times (11 + 5) \times 8 = \frac{1}{2} \times 16 \times 8 = 64\ \text{cm}^2
$$

✔ Answer:
Perimeter = 33.69 cm, Area = 64 cm²

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4.

- Sides: 4 cm, 7.73 cm, 6.81 cm, 10 cm
- Height: 7 cm
- Bases: top = 4 cm, bottom = 10 cm

Perimeter:
$$
P = 4 + 7.73 + 6.81 + 10 = 28.54\ \text{cm}
$$

Area:
$$
A = \frac{1}{2} \times (4 + 10) \times 7 = \frac{1}{2} \times 14 \times 7 = 49\ \text{cm}^2
$$

✔ Answer:
Perimeter = 28.54 cm, Area = 49 cm²

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5.

- Sides: 4 cm, 6.24 cm, 5.13 cm, 11 cm
- Height: 5 cm
- Bases: top = 4 cm, bottom = 11 cm

Perimeter:
$$
P = 4 + 6.24 + 5.13 + 11 = 26.37\ \text{cm}
$$

Area:
$$
A = \frac{1}{2} \times (4 + 11) \times 5 = \frac{1}{2} \times 15 \times 5 = 37.5\ \text{cm}^2
$$

✔ Answer:
Perimeter = 26.37 cm, Area = 37.5 cm²

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6.

- Sides: 15 cm, 9.45 cm, 7.40 cm, 6 cm
- Height: 7 cm
- Bases: top = 15 cm, bottom = 6 cm

Perimeter:
$$
P = 15 + 9.45 + 7.40 + 6 = 37.85\ \text{cm}
$$

Area:
$$
A = \frac{1}{2} \times (15 + 6) \times 7 = \frac{1}{2} \times 21 \times 7 = 73.5\ \text{cm}^2
$$

✔ Answer:
Perimeter = 37.85 cm, Area = 73.5 cm²

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7.

- Sides: 6 cm, 6.37 cm, 6.46 cm, 1 cm
- Height: 6 cm
- Bases: top = 6 cm, bottom = 1 cm

Perimeter:
$$
P = 6 + 6.37 + 6.46 + 1 = 19.83\ \text{cm}
$$

Area:
$$
A = \frac{1}{2} \times (6 + 1) \times 6 = \frac{1}{2} \times 7 \times 6 = 21\ \text{cm}^2
$$

✔ Answer:
Perimeter = 19.83 cm, Area = 21 cm²

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8.

- Sides: 3 cm, 4.21 cm, 4.48 cm, 5 cm
- Height: 4 cm
- Bases: top = 3 cm, bottom = 5 cm

Perimeter:
$$
P = 3 + 4.21 + 4.48 + 5 = 16.69\ \text{cm}
$$

Area:
$$
A = \frac{1}{2} \times (3 + 5) \times 4 = \frac{1}{2} \times 8 \times 4 = 16\ \text{cm}^2
$$

✔ Answer:
Perimeter = 16.69 cm, Area = 16 cm²

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9.

- Sides: 16 cm, 9.22 cm, 9.39 cm, 2 cm
- Height: 7 cm
- Bases: top = 16 cm, bottom = 2 cm

Perimeter:
$$
P = 16 + 9.22 + 9.39 + 2 = 36.61\ \text{cm}
$$

Area:
$$
A = \frac{1}{2} \times (16 + 2) \times 7 = \frac{1}{2} \times 18 \times 7 = 63\ \text{cm}^2
$$

✔ Answer:
Perimeter = 36.61 cm, Area = 63 cm²

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✔ Final Answers Summary:

| # | Perimeter (cm) | Area (cm²) |
|---|----------------|------------|
| 1 | 12.69 | 9 |
| 2 | 22.71 | 30 |
| 3 | 33.69 | 64 |
| 4 | 28.54 | 49 |
| 5 | 26.37 | 37.5 |
| 6 | 37.85 | 73.5 |
| 7 | 19.83 | 21 |
| 8 | 16.69 | 16 |
| 9 | 36.61 | 63 |

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📝 Notes:

- All shapes are trapezoids with two parallel sides (bases).
- The dashed lines represent the height (perpendicular to the bases).
- Always ensure units are consistent (all in cm here).

Let me know if you'd like this as a printable answer sheet!