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 lengths: 3.76 and 5 (but we only need base and height)
$$
A = \text{base} \times \text{height} = 5 \times 2 = 10
$$
✔ Answer: 10
---
Problem 2: Trapezoid
Given:
- Bases: 9 (bottom) and 5 (top)
- Height = 2.03 (the perpendicular distance between bases)
- Other side: 2.84 (not needed for area)
$$
A = \frac{1}{2} \times (9 + 5) \times 2.03 = \frac{1}{2} \times 14 \times 2.03 = 7 \times 2.03 = 14.21
$$
✔ Answer: 14.21
---
Problem 3: Trapezoid
Given:
- Bases: 16 (bottom), 7 (top)
- Height = 3.94 (perpendicular height from top to bottom)
- Other sides: 6.35 and 4 (not needed)
$$
A = \frac{1}{2} \times (16 + 7) \times 3.94 = \frac{1}{2} \times 23 \times 3.94 = 11.5 \times 3.94
$$
Now calculate:
$$
11.5 \times 3.94 = (10 + 1.5) \times 3.94 = 39.4 + 5.91 = 45.31
$$
✔ Answer: 45.31
---
Problem 4: Parallelogram
Given:
- Base = 14
- Height = 2 (vertical line labeled 2)
- Sides: 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 (perpendicular from vertex to base)
- Other sides: 6 and 8 (not needed)
$$
A = \frac{1}{2} \times 11 \times 4.50 = 5.5 \times 4.50
$$
Calculate:
$$
5.5 \times 4.5 = (5 + 0.5) \times 4.5 = 22.5 + 2.25 = 24.75
$$
✔ Answer: 24.75
---
Problem 6: Trapezoid
Given:
- Bases: 8 (bottom), 4 (top)
- Height = 2.53 (perpendicular height)
- Other sides: 2.36 and 2.53 (wait — note: the 2.53 is likely the height, not a side)
So:
- Base₁ = 8
- Base₂ = 4
- Height = 2.53
$$
A = \frac{1}{2} \times (8 + 4) \times 2.53 = \frac{1}{2} \times 12 \times 2.53 = 6 \times 2.53 = 15.18
$$
✔ Answer: 15.18
---
✔ Final Answers:
1.
10
2.
14.21
3.
45.31
4.
28
5.
24.75
6.
15.18
---
🔍 Explanation Summary:
- For
parallelograms, use
base × height.
- For
triangles, use
½ × base × height.
- For
trapezoids, use
½ × (sum of bases) × height.
- Always identify the
height as the perpendicular distance between bases or from vertex to base.
Let me know if you'd like these answers formatted in a printable way!
Parent Tip: Review the logic above to help your child master the concept of area of a triangle worksheet 5th grade.
