Swap the shortest and longest pencil's places. You don't have to move the middle pencil.
4/3 of the area of the larger hexagon to the area of the smaller hexagon
Let the sides of the interior hexagon be 2 cm long, then this hexagon is made up of 6 equilateral triangles of side = 2.
The area of this hexagon = 6 * 1 * sqrt3 = 6 sqrt3 ( as the triangle is made up of 2 60-30-90 triangles)
The exterior hexagon is made up of 6 equilateral triangles with altitude 2 and the area = 6 * 2 * (2 / sqrt3 ) = 24 / sqrt3
area exterior hex / interior hex = 24 / sqrt3 * 1 / 6sqrt3 = 24/18
= 4/3
Required ratio = 4/3 answer
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Answer:
Let's simplify step-by-step.
3a − 2 ( 8 + 4a )
Distribute:
= 3a + ( −2 ) ( 8 ) + ( −2 ) ( 4a )
= 3a + −16 + −8a
Combine Like Terms:
= 3a + −16 + −8a
= ( 3a + −8a ) + ( −16 )
Answer:
= −5a − 16
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