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A section of land is in the shape of a trapezoid. The two parallel sides measure 1.7 kilometers and 2.4 kilometers. The perpendicular distance between these sides is 0.75 kilometers.

What is the area of the land? Round to the nearest hundredth.

A. 1.53 km²
B. 2.43 km²
C. 3.06 km²
D. 4.85 km²



Answer :

GinnyAnswer
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]

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