To solve the problem, let's follow the steps systematically:
1. Identify the given values:
- [tex]\( AB = 6.3 \)[/tex] cm (one side of the parallelogram)
- [tex]\( AD = 4.9 \)[/tex] cm (another side of the parallelogram)
- [tex]\( AN = 4.2 \)[/tex] cm (perpendicular height from point A to side [tex]\( CD \)[/tex])
2. Calculate the area of the parallelogram:
- The area of a parallelogram can be determined by the formula:
[tex]\[
\text{Area} = \text{base} \times \text{height}
\][/tex]
- In this case, if we consider [tex]\( AB \)[/tex] as the base and [tex]\( AN \)[/tex] as the height from vertex A to side [tex]\( CD \)[/tex]:
[tex]\[
\text{Area} = AB \times AN
\][/tex]
- Substitute the given values:
[tex]\[
\text{Area} = 6.3 \, \text{cm} \times 4.2 \, \text{cm}
\][/tex]
- Calculate the result:
[tex]\[
\text{Area} = 6.3 \times 4.2 = 26.46 \, \text{cm}^2
\][/tex]
3. Find the perpendicular height [tex]\( AM \)[/tex]:
- The area of the parallelogram can also be expressed using the other side [tex]\( AD \)[/tex] as the base and [tex]\( AM \)[/tex] as the corresponding height:
[tex]\[
\text{Area} = AD \times AM
\][/tex]
- Since the area is already known from the previous calculation,
[tex]\[
26.46 \, \text{cm}^2 = 4.9 \, \text{cm} \times AM
\][/tex]
- Solve for [tex]\( AM \)[/tex]:
[tex]\[
AM = \frac{26.46 \, \text{cm}^2}{4.9 \, \text{cm}} = 5.4 \, \text{cm}
\][/tex]
4. Conclusion:
- The area of the parallelogram [tex]\( ABCD \)[/tex] is [tex]\( 26.46 \, \text{cm}^2 \)[/tex].
- The length of the perpendicular [tex]\( AM \)[/tex] from A to BC is [tex]\( 5.4 \, \text{cm} \)[/tex].
By following these steps, we've calculated the area of the parallelogram and found the length of [tex]\( AM \)[/tex] successfully.
