$解：∵ 四邊形?ABCD?是菱形$
$∴? AB=AD=CD=BC，??AC⊥BD，?$
$?OA=OC，??OB=OD?$
$∵ 菱形?ABCD?的周長為?20\ \mathrm {cm}?$
$∴? AD=\frac 1 4×20=5\ \mathrm {cm}?$
$∵? AC=8\ \mathrm {cm}?$
$∴? OA=\frac 1 2AC=4\ \mathrm {cm}?$
$在?Rt△OAD?中，∵? AD=5\ \mathrm {cm}，??OA=4\ \mathrm {cm}?$
$∴? OD={\sqrt {{AD}^2-{OA}^2}}=3\ \mathrm {cm}?$
$∴? BD=2OD=6\ \mathrm {cm}，??{S}_{菱形ABCD}={\frac {1} {2}}AC×BD={\frac {1} {2}×6×8=24{cm}^2}?$
