In the isosceles trapezoid ABCD, the upper base ad = 2, the lower base = 8, and M is the midpoint of the waist ab. if MD is perpendicular to CD, the trapezoid area can be calculated

In the isosceles trapezoid ABCD, the upper base ad = 2, the lower base = 8, and M is the midpoint of the waist ab. if MD is perpendicular to CD, the trapezoid area can be calculated

DQ over D ⊥ BC over Q
Make point n in CD, connect Mn, and cross DQ to s
Mn is a trapezoidal ABCD median line
∴MN=5,MN‖BC
The MS is a trapezoidal abqd median line
Ms = 7 / 2, s is the midpoint of DQ
∵DQ⊥BC,MN‖BC
∴DQ⊥MN
Let DS = sq = a
Then MS & sup2; + PS & sup2; = MD & sup2;
Then MP & sup2; = 49 / 4 + A & sup2;
SN is the median line of △ DQC
∴SN=3/2
∴DN²=9/4 +a²
∵MD⊥CD
∴MD²+DN²=MN²
∴49/4 + a²+ 9/4 +a²=25
The solution is a = √ 21 / 2
DQ=√21
S=1/2(2+8)*√21=5√21