Problem Solving

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avenus wrote:..

The area of the inner triangle = sqrt(3)/4*6^2 =9*Sqrt(3)

Side length of bigger triangle = 6+ 2*2+2 = 12 (See the picture, the shaded triangle is 60-30-90 with side against 60 measuring sqrt(3) , the other sides are 1 (opposite to 30 degrees) and 2)

Area of the bigger triangle = 36*Sqrt(3)

Area of the strip = 27*Sqrt(3)

ajith wrote:

avenus wrote:..

The area of the inner triangle = sqrt(3)/4*6^2 =9*Sqrt(3)

Side length of bigger triangle = 6+ 2*2+2 = 12 (See the picture, the shaded triangle is 60-30-90 with side against 60 measuring sqrt(3) , the other sides are 1 (opposite to 30 degrees) and 2)

Area of the bigger triangle = 36*Sqrt(3)

Area of the strip = 27*Sqrt(3)

Ajith,

Could you explain this : Side length of bigger triangle = 6+ 2*2+2 = 12.

I used 6+2*2 for the side of larger triangle. However, I notice you have added it to a 2 again, unable to understand the reason.

ajith wrote:

avenus wrote:..

The area of the inner triangle = sqrt(3)/4*6^2 =9*Sqrt(3)

Side length of bigger triangle = 6+ 2*2+2 = 12 (See the picture, the shaded triangle is 60-30-90 with side against 60 measuring sqrt(3) , the other sides are 1 (opposite to 30 degrees) and 2)

Area of the bigger triangle = 36*Sqrt(3)

Area of the strip = 27*Sqrt(3)

Please refer to the picture - there is a shaded triangle and a rhombus at the bottom.

Side of the bigger triangle = side of the smaller triangle + 2*side of the rhombus +2* base of the shaded triangle

Now 30-60-90 shaded triangle has the sides in 1:sqrt(3):2 and the height is sqrt(3) => base of the shaded triangle = 1 and side of the rhombus = 2

Side of the bigger triangle = 6+ 2*2+2*1