1) Draw any equilateral triangle. Join the midpoints of its sides. How many regular polygons are formed? Name them.
2) Draw. (i) A regular hexagon (ii) A regular octagon, Join their alternate vertices and name the figure formed with maximum number of sides.
Answers
Answer:
Area of an equilateral triangle of side a is given by
3
4
a
2
Now, the side of the equilateral triangle formed by joining the midpoints of the original triangle is
2
a
Hence, the corresponding area is
3
4
(
2
a
)
2
Similarly, the side of next triangle inside this triangle will be
4
a
Hence, its area will be
3
4
(
4
a
)
2
So, the sum of all these areas is an infinite geometric series with first term as
3
4
a
2
and with common ratio 1/4
Sum of infinite geometric series is
1−commonratio
firstterm
(
1−r
a
)
Given that the side of the original triangle is 18 cm
Hence, a=
4
3
(18)
2
=81
3
and r=
4
1
Putting the values of a and r in the formula and rationalizing, we get the answer as 108
3
Answer:square
Step-by-step explanation:tilt your octagon and join the vertices