in a Trapezium ABCD ab parallel CD BD perpendicular a d and ac perpendicular BC if ad is equal to BC is equal to 15 cm and a b is equal to 25 cm find the area of trapezium a b c d
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Answer:
Step-by-step explanation:
Our question is: in a Trapezium ABCD ab parallel CD BD perpendicular a d and ac perpendicular BC if ad is equal to BC is equal to 15 cm and a b is equal to 25 cm find the area of trapezium a b c d.
Translate D by vector AB, and let its image be E. Quadrilateral ABED is a parallelogram, so EB is equal in length to DA. Now consider triangle EBC. All three sides are known.
EB = 13 cm
BC = 15 cm
CE = 14 cm
Use Heron's formula. For triangles that is. There is no Heron's formula for quadrilaterals.
(13 + 15 + 14)/2 = 21
area(EBC) = √[21(21 - 13)(21 - 15)(21 - 14)]
= √[21(8)(6)(7)]
= √(7056)
= 84
Let EC be the base of that triangle. Find its corresponding height.
(base)(height)/2 = area
14h/2 = 84
h = 12
The height of triangle EBC is 12 cm. That is also the height of the trapezium.
area(ABCD) = (AB + DC)h/2
= (30 + 44)(12)/2
= 444 cm²
Hence, our area is equal to 444cm².
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Answer:
We can find out the area of triangle ADB
so height for this triangle wud be equal to the height of trapezium.
so we get height = 12cm.
now we can easily get to CD=7cm
and we know area of trapezium =1/2*(AB+CD)*HEIGHT
NOW,1/2*(25+7)*12 = 192 cm.
how to get CD=7 cm
when we will drop two perpendicular lines from D to AB as point E and from C to AB as point F.
So,we can see that EF = CD (as the line drawns were perpendicular)
Now In triangleADE,
We know AD=15 and DE=12
So we can easily find AE = 9
Similarly from triangleBCF,
we will get BF = 9cm
therefore,EF = AB -(AE+BF) = 25 - 18 =7cm.
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