Question

In the figure shown, BC is parallel to
AD and AB =
AB = CD. What is the
perimeter of quadrilateral ABCD ?

Answer 1

Answer:

52 units.

Step-by-step explanation:

If we drop a perpendicular line from point C to AD and call the point ( on AD) E we have a right triangle CED.

Now CE = 6 and as the whole figure is symmetrical about the dashed line,

ED = (26 - 10)/2

= 8.

So by Pythagoras:

CD^2 = 6^2 + 8^2 = 100

CD = 10.

So, as AB = CD,

the perimeter = 10 + 26 + 2(8)

= 52.

Answer 2

The perimeter of the Quadrilateral ABCD is 56

Given that :

BC = 10

AD = 26

AM = ND = (26 - 10) / 2 = 16 / 2 = 8

Using Pythagoras:

AB² = AM² + BM²

AB² = 8² + 6²

AB² = 64 + 36

AB² = 100

AB = √100

AB = 10

AB = CD = 10

THE PERIMETER OF THE QUADRILATERAL WILL BE :

AB + BC + CD + AD

10 + 10 + 26 + 10 = 56

HENCE, The PERIMETER of the quadrilateral ABCD = 56

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