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Maths-

General

Easy

Question

A Square of side 4 units is combined with two right angled triangles of bases each 3units to form a Trapezium (as shown in figure). Then perimeter of the Trapezium is

14 units
24 units
16 units
22 units

hint Hint:

Find the all side length of trapezium to find the perimeter. Find the non parallel sides of trapezium by using pythagoras theorem.

The correct answer is: 24 units

Given, A Square of side 4 units is combined with two right angled triangles of bases each 3units to form a Trapezium (as shown in figure).
Side of square = BC =CD = DA = 4units
Using pythagoras theorem,
$A Y space equals square root of A D squared space plus space D Y squared end root space space text and end text space space B X space equals square root of B C squared space plus space C X squared end root A Y space equals space square root of 4 squared plus 3 squared end root space equals space square root of 25 space equals space 5 space text and end text space B X space equals space square root of 4 squared plus 3 squared end root space equals space square root of 25 space equals space 5$
We get sides AY = 5 units and BX = 5 units
YX = YD +DC + CX = 3 + 4 + 3 = 10 units
perimeter = YX + XB + BA + AY = 10 + 5 + 4 +5 = 24 units
Therefore, perimeter of the Trapezium is 24 units.

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