Grade 5 Worksheets: Area of triangles, parallelograms, trapezoids ... - Free Printable

Let's solve each problem on the worksheet step by step. The worksheet asks us to find the area of various shapes: triangles, parallelograms, and trapezoids.

We will use the following formulas:

1. Area of a triangle:
$$
A = \frac{1}{2} \times \text{base} \times \text{height}
$$

2. Area of a parallelogram:
$$
A = \text{base} \times \text{height}
$$

3. Area of a trapezoid:
$$
A = \frac{1}{2} \times (\text{base}_1 + \text{base}_2) \times \text{height}
$$

---

Problem 1: Parallelogram

Given:
- Base = 5
- Height = 2 (the perpendicular height is labeled as 2)
- Side = 3.76 (not needed)

$$
A = \text{base} \times \text{height} = 5 \times 2 = 10
$$

✔ Answer: 10

---

Problem 2: Trapezoid

Given:
- Bases: 9 (bottom), 5 (top)
- Height = 2.03 (perpendicular distance between bases)

$$
A = \frac{1}{2} \times (9 + 5) \times 2.03 = \frac{1}{2} \times 14 \times 2.03 = 7 \times 2.03 = 14.21
$$

✔ Answer: 14.21

---

Problem 3: Trapezoid

Given:
- Bases: 16 (bottom), 7 (top)
- Height = 4 (perpendicular height shown)
- Sides: 3.94 and 6.35 (not needed)

$$
A = \frac{1}{2} \times (16 + 7) \times 4 = \frac{1}{2} \times 23 \times 4 = 11.5 \times 4 = 46
$$

✔ Answer: 46

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Problem 4: Parallelogram

Given:
- Base = 14
- Height = 2 (vertical height shown)
- Other side = 5.27 and 6.32 (not needed)

$$
A = \text{base} \times \text{height} = 14 \times 2 = 28
$$

✔ Answer: 28

---

Problem 5: Triangle

Given:
- Base = 11
- Height = 4.50 (altitude from base to opposite vertex)

$$
A = \frac{1}{2} \times 11 \times 4.50 = 5.5 \times 4.50 = 24.75
$$

✔ Answer: 24.75

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Problem 6: Trapezoid

Given:
- Bases: 8 (bottom), 4 (top)
- Height = 2.36 (perpendicular height)
- Other sides: 2.53 and 2.36 — note that 2.36 appears again, but it’s likely the height

Wait: Let's check carefully.

The shape has:
- Top base = 4
- Bottom base = 8
- Height = 2.36 (labeled as vertical line from top to bottom)
- Sides: 2.53 and 2.36 — but 2.36 is likely the height

So,
$$
A = \frac{1}{2} \times (4 + 8) \times 2.36 = \frac{1}{2} \times 12 \times 2.36 = 6 \times 2.36 = 14.16
$$

✔ Answer: 14.16

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✔ Final Answers:

1. 10
2. 14.21
3. 46
4. 28
5. 24.75
6. 14.16

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