Question

Regular hexagon ABCDEF has vertices at A(4,4√3), B (8,4√3), C (10,2√3),D(8,0),E(4,0) and F (2,2√3). Suppose the sides of the hexagon are reduced by 40% to produce a similar regular hexagon. What are the perimeter and are of the smaller hexagon rounded to the nearest tenth? Explain how you found your answer.

Answer 1

P=Small =6a small =6x2.4 =14.4 unit

Answer 2

The original hexagon's perimeter is calculated by adding the lengths of all six sides, which gives a value of approximately 32.15 units. Reducing the sides by 40% results in a new perimeter of approximately 19.29 units.

The area of the smaller hexagon can be found by squaring the scaling factor (0.6) and multiplying it by the area of the original hexagon. This gives an approximate area of 50.9 square units for the smaller hexagon.

Answer 3

in Regular hexagon all six sides are equal.
\[AB=\sqrt{(8-4)^2+(4\sqrt{3}-4\sqrt{3})^2}=4\]
perimeter=6*4=24
100-40=60
small perimeter=60 % *24=14.40

Answer 4

\[\frac{ h }{ 2 }=\tan 60\]
\[h=2\tan 60=2\times \sqrt{3}=2\sqrt{3}\]
area of one triangle
\[=\frac{ 1 }{ 2 }\times 4 \times 2\sqrt{3}=4\sqrt{3} ~sq.~units\]
area of regular hexagon
\[=6\times 4\sqrt{3}=24\sqrt{3}\approx 24\times 1.732 \approx 41.568 \approx 41.57~sq.units\]

Answer 5

To find the new coordinates of the vertices after reducing the sides by 40%, I multiplied the x-coordinates and y-coordinates of each vertex by 0.6 (which is 1 - 0.4). Then, I used the new coordinates to calculate the distances between the vertices to find the perimeter of the smaller hexagon. Finally, I used the formula for the area of a regular hexagon (Area = (3√3 * s^2) / 2) to find the area of the smaller hexagon. After performing the calculations, I found the perimeter of the smaller hexagon to be approximately 15.5 units and the area to be approximately 46.8 square units.