# Can u solve: 15. A regular hexagon is having side of 12 cm. Find the area of the hexagon.  16.. In a trapezium. one of the parallel sides is half of the other. The height is 4 cm. If the area of the trapezium is 36 sq.cm, then what are the lengths of the parallel sides?

For remaining queries we request you to post them in separate threads to have rapid assistance from our experts.

Regards

• 1
15. Given it is a regular hexagon with side 12 cm.
​This regular word shows that all the sides of the hexagon are same ie. 12 cm.
​Now if we divide a regular hexagon it gives us 6 equilateral triangles of all sides 12 cm.

​As we all know area of equilateral triangles without height = (Root 3/4) aunit​2
​Where a = Side of the triangle (Equilateral)

By putting the values we get = (Root 3/4) 122
​So the answer will be = 0.433...*144
Area = 62.3538 cm​2

​At the start we got 6 equilateral triangles so we have to multiply 6 to the value of Area of one equilateral triangle
​ie. 62.3538 cm* 6
Thus Area of Hexagon = 374.1228 cm2

16. Here Height = 4 cm , Parrallel sides => 1st=x ,2nd = x/2 And Area = 36 cm2
​Area of Trapezium = 1/2 *(Sum of parrallel sides) * height

​​So by putting the values to the above formula, it gives us
(x+x/2)/2 * 4 = 36 cm​2    ( By shifting 4 to other side of equal to RHS)
​(x+x/2)/2 = 36/4 ==> 1/2 * (x+x/2) = 9*2  (By shifting 2 to other side RHS)
​(2x+x)/2=18 ==> (By taking 2 to other side RHS)
3x=18*2 ==> 3x=36 (By taking 3 to RHS)
x=12

​Put the value of x to the given parrallel sides in the question
ie x and x/2
​Thus, The parrallel sides will be 12cm and 6 cm
For proof use these values in the formula ie 1/2 * (12+6) * 4
Area of Trapezium = 9*4 = 36cm2 Hence proved
​Hence, The 2 parrallel sides are 6cm and 12 cm respectively.
I hope it has helped you...

• 2
What are you looking for?