Answer:
The height of trapezoid is 7km.
Explanation:
Given that the area of trapezoid formula is A = 1/2×(a+b)×h where a and b represents the length and h is the height. By substituing the values, you are able to find the height :
![area = (1)/(2) * (a + b) * h](https://img.qammunity.org/2021/formulas/mathematics/middle-school/qexjprq7moqv5h27pttedehjvlj4w2qo74.png)
Let a = 4km,
Let b = 8km,
Let area = 42km²,
![42 = (1)/(2) * (4 + 8) * h](https://img.qammunity.org/2021/formulas/mathematics/middle-school/pq2xkrdkg8k9am2rpsrn848h210q6rnmgk.png)
![42 = (1)/(2) * 12 * h](https://img.qammunity.org/2021/formulas/mathematics/middle-school/6b3sm70v2pna013j5f5ugiohd6xfex78z8.png)
![42 = 6 * h](https://img.qammunity.org/2021/formulas/mathematics/middle-school/onmn5efyx7h9nw519pi9swn97y2vpifgga.png)
![6h = 42](https://img.qammunity.org/2021/formulas/mathematics/middle-school/hj6l6byba2uzmi469px265znicn0pqx80v.png)
![h = 7 \: km](https://img.qammunity.org/2021/formulas/mathematics/middle-school/ukd0ltk1vpjlp0bfxxk7gw03a24d5ku4zv.png)