Certainly! Let's solve this problem step-by-step.
Given:
- Parallelogram [tex]\(ABCD\)[/tex] with [tex]\(AB = 18 \, \text{cm}\)[/tex] and [tex]\(BC = 12 \, \text{cm}\)[/tex]
- [tex]\(AL\)[/tex] is perpendicular to [tex]\(DC\)[/tex] and [tex]\(AL = 6.4 \, \text{cm}\)[/tex]
- [tex]\(AM\)[/tex] is perpendicular to [tex]\(BC\)[/tex]
Step 1: Calculate the area of the parallelogram.
- The area of a parallelogram can be calculated using the base and the corresponding height.
- Here, we can use side [tex]\(AB\)[/tex] as the base and [tex]\(AL\)[/tex] as the height corresponding to [tex]\(AB\)[/tex].
[tex]\[ \text{Area} = AB \times AL \][/tex]
[tex]\[ \text{Area} = 18 \, \text{cm} \times 6.4 \, \text{cm} \][/tex]
[tex]\[ \text{Area} = 115.2 \, \text{cm}^2 \][/tex]
Step 2: Calculate [tex]\(AM\)[/tex], the height corresponding to side [tex]\(BC\)[/tex].
- Since the area of the parallelogram is the same regardless of which pair of base and height is used, we can use the calculated area with base [tex]\(BC\)[/tex] to find the height [tex]\(AM\)[/tex].
[tex]\[ \text{Area} = BC \times AM \][/tex]
[tex]\[ 115.2 \, \text{cm}^2 = 12 \, \text{cm} \times AM \][/tex]
Now, solve for [tex]\(AM\)[/tex]:
[tex]\[ AM = \frac{115.2 \, \text{cm}^2}{12 \, \text{cm}} \][/tex]
[tex]\[ AM = 9.6 \, \text{cm} \][/tex]
So, the length of [tex]\(AM\)[/tex] is [tex]\(9.6 \, \text{cm}\)[/tex].
