Question

Two parallel sides of an isosceles trapezium are 31cm and 15cm it's non parallel side are each equal 17cm find the area of the trapezium

Answer 1

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,

$AC^2=AE^2+CE^2$

$17^2=AE^2+8^2$

$289=AE^2+64$

$AE=\sqrt{225}$

$AE=15$

The height of trapezium is 15 cm.

The area of the trapezium is

$A=\frac{1}{2}\times \text{Sum of parallel side}\times \text{Height}$

$A=\frac{1}{2}\times (31+15)\times 15$

$A=\frac{1}{2}\times 46\times 15$

$A=345$

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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