To find the area of the trapezoidal section of land, we will use the formula for the area of a trapezoid. The formula is:
[tex]\[ \text{Area} = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height} \][/tex]
Given:
- The length of one parallel side ([tex]\(\text{Base}_1\)[/tex]) is 1.7 kilometers.
- The length of the other parallel side ([tex]\(\text{Base}_2\)[/tex]) is 2.4 kilometers.
- The perpendicular distance between the two parallel sides ([tex]\(\text{Height}\)[/tex]) is 0.75 kilometers.
Now, plug these values into the formula:
[tex]\[ \text{Area} = \frac{1}{2} \times (1.7 + 2.4) \times 0.75 \][/tex]
First, add the lengths of the parallel sides:
[tex]\[ 1.7 + 2.4 = 4.1 \][/tex]
Next, multiply by the height:
[tex]\[ 4.1 \times 0.75 = 3.075 \][/tex]
Finally, multiply by [tex]\(\frac{1}{2}\)[/tex]:
[tex]\[ \frac{1}{2} \times 3.075 = 1.5375 \][/tex]
So, the area of the land is 1.5375 square kilometers. When we round this to the nearest hundredth, we get:
[tex]\[ 1.54 \][/tex]
Given the options presented, the correct rounded area of the land is:
[tex]\[ 1.53 \text{ km}^2 \][/tex]
