Question

In the given figure ABCD is parallelogram in which DC=10cm and BC=4root3cm. AP is perpendicular to DC. If
angle ADC = 60. Find:
(1) length of AP
(ii) Area of parallelogram ABCD
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Answer 1

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Answer 2

Given:  ABCD is a parallelogram in which DC=10cm and BC=4root3cm. AP is perpendicular to DC and angle ADC = 60.

To find: Length of AP and Area of the parallelogram ABCD

Solution:

In a parallelogram, the opposite sides are always parallel and equal to the opposite side.

So the sides BC and AD= 4 root 3cm

And the sides AB and CD= 10 cm

Since, AP is perpendicular on CD so in triangle DAP,

angle APD+ angle ADP+ Angle DAP= 180 Degrees

90 degrees+60 degrees+ angle DAP= 180 degrees

Angle DAP= 180 degrees-150 degrees

Angle DAP=30

Now, to find AP, sin30 degrees= Perpendicular/Hypotenuse

Sin30 degrees= AP/4root3 = 1/2 into 4 root3= 2 root 3= AP

Area of parallelogram ABCD= base into height= 2 root 3 into 10= 20root3

Length of AP= 2root3

Area of parallelogram ABCD= 20root3

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