its perimeter. (a) In figure (i) given below, AB || DC, BC = AD = 13 cm, AB = 22 cm and DC = 12 cm. Calculate the height of the trapezium ABCD.
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Answer:
Hence the height of the trapezium is 12 cm.
Step-by-step explanation:
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Class 8
>>Maths
>>Understanding Quadrilaterals
>>Kinds of Quadrilateral
>>In figure (i) given below, AB || DC, BC
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In figure (i) given below, AB∣∣DC,BC=AD=13 cm,AB=22 cm and DC=12 cm. Calculate the height of the trapezium ABCD.
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Given AB∣∣DC,BC=AD=13 cm
AB=22 cm and DC=12 cm
Here, DC=12
So, MN=12 cm
Also, AM=BN
AB=AM+MN+BN
22=AM+12+AM[∵AM=BN]
2AM=22−12
2AM=10
AM=
2
10
AM=5 cm
We know that AMD is a right triangle.
AD
2
=AM
2
+DM
2
[Pythagoras theorem]
13
2
=52+DM
2
DM
2
=13
2
−52
DM
2
=169−25
DM
2
=144
Taking square root on both sides,
DM=12 cm
Hence the height of the trapezium is 12 cm
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