![HG = 5](/tpl/images/0701/3436/76bce.png)
Step-by-step explanation:
Given
![HE = 8mm](/tpl/images/0701/3436/072c1.png)
![EF = 12mm](/tpl/images/0701/3436/b95d0.png)
![Area = 68mm^2](/tpl/images/0701/3436/e7456.png)
Find the length of HG
First, it should be noted that the displayed figure is a trapezium
The area of a trapezium is calculated by multiplying the sum of parallel sides by half its height;
In this case;
![Area = \frac{HG + EF}{2} * HE](/tpl/images/0701/3436/f261c.png)
Substitute the values of Area, HE and EF
![68 = \frac{HG + 12}{2} * 8](/tpl/images/0701/3436/cf47d.png)
![68 = (HG + 12) * 4](/tpl/images/0701/3436/14354.png)
Divide both sides by 4
![\frac{68}{4} = \frac{(HG + 12) * 4}{4}](/tpl/images/0701/3436/31676.png)
![17 = HG + 12](/tpl/images/0701/3436/7808c.png)
Subtract 12 from both sides
![17 - 12 = HG + 12 - 12](/tpl/images/0701/3436/20509.png)
![5 = HG](/tpl/images/0701/3436/af9ab.png)
![HG = 5](/tpl/images/0701/3436/76bce.png)
Hence, the length of HG is 5mm