Answer:
![(1)/(2)* \text{Boundary of county Harding touching Adams}* \text{Boundary of county Lincoln touching Adams}](https://img.qammunity.org/2020/formulas/mathematics/middle-school/93kj0eio6hcub1fq1mk63p1tvmpykll622.png)
Explanation:
In the figure attached, map shows the dimensions of the 5 counties in a Midwestern state.
Adams county has the triangular boundaries.
Since area of triangle is represented by the expression
![(1)/(2)(\text{Base})* (\text{Height})](https://img.qammunity.org/2020/formulas/mathematics/middle-school/776yjqip2mhfb48ql0cembyiqvf3zz9t9f.png)
Base represents the boundary of county Harding touching Adams = 18 mi.
Height represents the boundary of county Lincoln touching Adams = 10 mi
Therefore, expression representing the area of Adams county will be
![(1)/(2)* \text{Boundary of county Harding touching Adams}* \text{Boundary of county Lincoln touching Adams}](https://img.qammunity.org/2020/formulas/mathematics/middle-school/93kj0eio6hcub1fq1mk63p1tvmpykll622.png)
=
![(1)/(2)18* 10](https://img.qammunity.org/2020/formulas/mathematics/middle-school/zwjfkntjbhrog7cwivgdrena44v42knvfq.png)
= 90 square miles.