问题1：如果是数字，则ABCD是平行四边形，AE⊥DC和CF⊥AD。如果AB = 16厘米，AE = 8厘米，CF = 10厘米，找到AD。
解决方案：
In parallelogram ABCD,
AB = CD = 16 cm {Since, opposite sides of a parallelogram are equal}
AE = 8 cm and CF = 10 cm
As we know,
Area of parallelogram = Base × Corresponding altitude
Area of parallelogram ABCD = CD × AE = AD × CF
16 × 18 = AD × 10
AD = 12.8
Thus, the length of AD = 12.8 cm
问题2：在问号中1，如果AD = 6厘米，CF = 10厘米，AE = 8厘米，找到AB。
解决方案：
In parallelogram ABCD,
AE = 8 cm, CF = 10 cm and AD = 6 cm
As we know, Area of parallelogram = Base x Corresponding altitude
Area of parallelogram ABCD = AD × CF = CD × AE
6 × 10 = CD × 8
CD = 6 × 10 = 60
8 8
CD = 7.5 cm = AB {Since, opposite sides of a parallelogram are equal}
Thus, the length of AB = 7.5 cm
问题3：让ABCD为面积为124 cm2的平行四边形。如果E和F分别是边AB和CD的中点，则求出平行四边形AEFD的面积。
解决方案：
ABCD be a parallelogram.
Given:
Area of parallelogram = 124 cm2
Construct AP perpendicular to DC
Now,
Area of parallelogram EBCF = FC x AP
and
Area of parallelogram AFED = DF x AP
Here F is the mid-point of DC,
so DF = FC
Hence,
Area of parallelogram AEFD = Area of parallelogram EBCF = (Area of parallelogram ABCD)
2
⇒ 124
2
⇒ 62
Area of parallelogram AEFD is 62 cm2.
问题4：如果ABCD是平行四边形，则证明
ar(ΔABD)= ar(ΔBCD)= ar(ΔABC)= ar( ΔACD)= 1 ar(|| gm ABCD)
2个
解决方案：
Given:
ABCD is a parallelogram.
To prove : ar(Δ ABD) = ar(Δ BCD) = ar(Δ ABC)=ar(Δ ACD) = 1 ar(||gm ABCD)
2
Proof:
When we join the diagonal of parallelogram, it divides it into two equilaterals.
Since, AC is the diagonal.
Step 1: Area (ΔABC) = Area (ΔACD) = 1 (Area of ||gm ABCD)
2
Since, BD is the diagonal
Step 2: Area (ΔABD) = Area (ΔBCD) = 1 ( Area of ||gm ABCD)
Now,
From the above steps
Area (ΔABC) = Area (ΔACD) = Area (ΔABD) = Area (ΔBCD) = 1 (Area of ||gm ABCD)
2
Hence Proved.