Question

In the given figure ABCD is a trapezium in which AD=13cm,BC=5cm,CD=17cm and angleA=angleB=90degree calculte 1.AB 2.Area of trapezium ABCD

Answer 1

1. AB = 15cm, 2)Area of trapezium =  $135\ cm^2$

Step-by-step explanation:

Given,AD = 13cm,BC = 5cm, CD = 17cm ,∠A =∠B =90°

Construction:

Draw a trapezium ABCD such that  DE perpendicular to BC which is parallel to AB.

Since,BC = BE + EC

         13cm = 5cm + 8 cm

Also,AD = 5cm

Since ∠A = ∠B = 90°

⇒AD ║ BC.

Now,In ΔDEC

∠DEC = 90°

By applyimg Pythagoras Theorem

$DC^2 = DE^2 + EC^2$

$(17)^2 = (DE)^2 + (8)^2$

$289 = (DE)^2 + 64$

$(DE)^2 = 289 - 64$

                 = 225

DE = 15cm

Also,AB = 15cm (Since AB is parallel and equal to DE)

In trapezium ABCD

AB is the height of trapezium parallel to BC.

Now,

Area of trapezium = $\frac{1}{2}\times (\textrm{sum of opposite parallel sides})\times\textrm{height}$

                              = $\frac{1}{2}\times (13cm + 5cm)\times 15cm$

                              = $\frac{1}{2}\times (18cm)\times 15cm$

                              = $135\ cm^2$

Answer 2

Step-by-step explanation:

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