Question

The local hardware store sells fencing for $1.30 per yard. If each unit on thegrid represents 25 yards, how much will it cost to fence in the plot of landrepresented by polygon MNOP?

Answer 1

To solve this problem, first, we have to find the distance of each side of the polygon MNOP.

From the graph, we know that NO = 3, and OP = 4.

However, for sides NM and MP we have to use the distance formula

`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

Let's find NM, where N(1,4) and M(-4,2).

`\begin{gathered} d_(NM)=√((-4-1)^2+(2-4)^2)=√((-5)^2+(-2)^2) \\ d_(NM)=√(25+4)=√(29)\approx5.4 \end{gathered}`

So, NM = 5.4.

Now, let's find MP, where M(-4,2) and P(4,0).

`\begin{gathered} d_(MP)=√((4-(-4))^2+(0-2)^2)=√((4+4)^2+(-2)^2) \\ d_(MP)=√(64+4)=√(68)\approx8.2 \end{gathered}`

MP = 8.2.

According to the problem, the unit of the grid represents 25 yards. So, let's multiply each distance by 25 to express it in yards.

`\begin{gathered} NO=3\cdot25=75yd \\ OP=4\cdot25=100yd \\ NM=5.4\cdot25=135yd \\ MP=8.2\cdot25=205yd \end{gathered}`

The problem also indicates that the cost per yard is $1.30, now let's multiply each distance with the cost, then we sum to find the total cost

`\begin{gathered} C=1.30(75+100+135+205) \\ C=1.30(515)=669.50 \end{gathered}`

Therefore, the total cost is $669.50, approximately.