please answer the question ASAP
In the given figure, ABCD is a trapezium in which
AD = 13 cm, BC = 5 cm, CD = 17 cm and
ZA = B = 90°
Calculate : (i) AB (ii) Area of trap. ABCD.
Answers
Answer:
1. AB = 15cm, 2)Area of trapezium = 135\ cm^2135 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^2DC
2
=DE
2
+EC
2
(17)^2 = (DE)^2 + (8)^2(17)
2
=(DE)
2
+(8)
2
289 = (DE)^2 + 64289=(DE)
2
+64
(DE)^2 = 289 - 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}
2
1
×(sum of opposite parallel sides)×height
= \frac{1}{2}\times (13cm + 5cm)\times 15cm
2
1
×(13cm+5cm)×15cm
= \frac{1}{2}\times (18cm)\times 15cm
2
1
×(18cm)×15cm
= 135\ cm^2135 cm
2