α=30o
|AC|=|DB|=a√2
1)
| 0.5a√2 | √2 | |||
W ΔSOB: cosβ= | = | ⇔β=45o | ||
| a | 2 |
| a√2 | ||
H= | ||
| 2 |
| |OP| | a√6 | |||
W ΔAOP: tg30o= | ⇔|OP|= | |||
| 0.5a√2 | 6 |
| |PS| | H | |PS| | 1 | |||||
ΔSKL∼ΔDBS⇔ | = | ⇔ | = | |||||
| |KL| | |DB| | |KL| | 2 |
| a√2 | a√6 | a(3√2−√6) | ||||
|PS|= | − | = | ||||
| 2 | 6 | 6 |
| a(3√2−√6) | ||
|KL|= | ||
| 3 |
| |AE| | |AC| | ||
= | ⇔ | ||
| sin(45o) | sin(180−(30+45)) |
| a√2*0.5√2 | ||
|AE|= | ||
| sin(75) |
| a | 4a*(√6−√2) | |||
|AE|= | = | |||
| 14*(√6+√2) | 6−2 |
| 1 | 1 | a(3√2−√6) | ||||
PALEK= | *|KL|*|AE|= | * | *a*(√6−√2) | |||
| 2 | 2 | 3 |
| a2*(4√3−6) | ||
PALEK= | ||
| 3 |