The parallel side of trapezium are 12cm and 17cm. if non-parallel side are equal. each being 6.5cm. find the Area of the trapezium
Answers
Answer:
The area of the trapezium is 345 cm².
Step-by-step explanation:
Given : Two parallel sides of an isosceles trapezium are 31 cm and 15 cm it's non parallel side are each equal 17 cm.
To find : The area of the trapezium ?
Solution :
Let the trapezium be ABCD, where AB// CD.
Two parallel sides of an isosceles trapezium are 31 cm and 15 cm.
So, AB=15 cm and CD=31 cm.
We draw two perpendiculars from A,B on CD point as E and F.
Refer the attached figure below.
AB=EF=15 cm
So, CE= FD=(31-15)/2=8 cm
The length of non-parallel side i.e. AC=BD=17 cm.
Applying Pythagoras theorem in ΔACE,
AC^2=AE^2+CE^2AC
2
=AE
2
+CE
2
17^2=AE^2+8^217
2
=AE
2
+8
2
289=AE^2+64289=AE
2
+64
AE=\sqrt{225}AE=
225
AE=15AE=15
The height of trapezium is 15 cm.
The area of the trapezium is
A=\frac{1}{2}\times \text{Sum of parallel side}\times \text{Height}A=
2
1
×Sum of parallel side×Height
A=\frac{1}{2}\times (31+15)\times 15A=
2
1
×(31+15)×15
A=\frac{1}{2}\times 46\times 15A=
2
1
×46×15
A=345A=345
Therefore, the area of the trapezium is 345 cm².
#Learn more
Two parallel side DC and ab of a trapezium are 12cm and 36cm respectively.if non parallel side are each equal to 15cm, find the area of trapezium.
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