Area of Parallelograms, Triangles, and Trapezoids worksheet with 16 figures for students to calculate area.

Here are the step-by-step solutions for each problem on the worksheet.

1. Parallelogram
* Formula: Area = Base × Height
* Calculation: $9 \text{ m} \times 4 \text{ m} = 36$
* Answer: $36 \text{ m}^2$

2. Parallelogram
* Formula: Area = Base × Height
* Calculation: $8 \text{ ft} \times 5 \text{ ft} = 40$
* Answer: $40 \text{ ft}^2$

3. Triangle
* Formula: Area = $\frac{1}{2} \times \text{Base} \times \text{Height}$
* Calculation: $\frac{1}{2} \times 7 \text{ in} \times 6 \text{ in} = 3.5 \times 6 = 21$
* Answer: $21 \text{ in}^2$

4. Triangle
* Formula: Area = $\frac{1}{2} \times \text{Base} \times \text{Height}$
* Calculation: $\frac{1}{2} \times 10 \text{ ft} \times 3 \text{ ft} = 5 \times 3 = 15$
* Answer: $15 \text{ ft}^2$

5. Trapezoid
* Formula: Area = $\frac{(b_1 + b_2)}{2} \times h$
* Calculation: Add bases ($3 + 5 = 8$), divide by 2 ($4$), multiply by height ($2$).
* $4 \times 2 = 8$
* Answer: $8 \text{ cm}^2$

6. Trapezoid
* Formula: Area = $\frac{(b_1 + b_2)}{2} \times h$
* Calculation: Add bases ($4 + 6 = 10$), divide by 2 ($5$), multiply by height ($4$).
* $5 \times 4 = 20$
* Answer: $20 \text{ m}^2$

7. Triangle
* Formula: Area = $\frac{1}{2} \times \text{Base} \times \text{Height}$
* Calculation: $\frac{1}{2} \times 12 \text{ mm} \times 10 \text{ mm} = 6 \times 10 = 60$
* Answer: $60 \text{ mm}^2$

8. Parallelogram
* Formula: Area = Base × Height
* Calculation: $8 \text{ km} \times 5 \text{ km} = 40$
* Answer: $40 \text{ km}^2$

9. Trapezoid
* Formula: Area = $\frac{(b_1 + b_2)}{2} \times h$
* Calculation: Add bases ($2 + 4 = 6$), divide by 2 ($3$), multiply by height ($3$).
* $3 \times 3 = 9$
* Answer: $9 \text{ in}^2$

10. Triangle
* Formula: Area = $\frac{1}{2} \times \text{Base} \times \text{Height}$
* Calculation: $\frac{1}{2} \times 12 \text{ yd} \times 4 \text{ yd} = 6 \times 4 = 24$
* Answer: $24 \text{ yd}^2$

11. Trapezoid
* Formula: Area = $\frac{(b_1 + b_2)}{2} \times h$
* Calculation: Add bases ($3 + 5 = 8$), divide by 2 ($4$), multiply by height ($4$).
* $4 \times 4 = 16$
* Answer: $16 \text{ ft}^2$

12. Triangle
* Formula: Area = $\frac{1}{2} \times \text{Base} \times \text{Height}$
* Calculation: $\frac{1}{2} \times 5 \text{ mi} \times 2 \text{ mi} = 2.5 \times 2 = 5$
* Answer: $5 \text{ mi}^2$

13. Trapezoid
* Formula: Area = $\frac{(b_1 + b_2)}{2} \times h$
* Calculation: Add bases ($5 + 8 = 13$), divide by 2 ($6.5$), multiply by height ($4$).
* $6.5 \times 4 = 26$
* Answer: $26 \text{ cm}^2$

14. Triangle
* Formula: Area = $\frac{1}{2} \times \text{Base} \times \text{Height}$
* Calculation: $\frac{1}{2} \times 6 \text{ ft} \times 4 \text{ ft} = 3 \times 4 = 12$
* Answer: $12 \text{ ft}^2$

15. Trapezoid
* Formula: Area = $\frac{(b_1 + b_2)}{2} \times h$
* Calculation: Add bases ($6 + 3 = 9$), divide by 2 ($4.5$), multiply by height ($7$).
* $4.5 \times 7 = 31.5$
* Answer: $31.5 \text{ in}^2$

16. Parallelogram
* Formula: Area = Base × Height
* Calculation: $9 \text{ yd} \times 6 \text{ yd} = 54$
* Answer: $54 \text{ yd}^2$

Final Answer:
1. 36 m²
2. 40 ft²
3. 21 in²
4. 15 ft²
5. 8 cm²
6. 20 m²
7. 60 mm²
8. 40 km²
9. 9 in²
10. 24 yd²
11. 16 ft²
12. 5 mi²
13. 26 cm²
14. 12 ft²
15. 31.5 in²
16. 54 yd²