Latest TCS Aptitude Question SOLUTION: A regular polygon with 12 sides (dodecagon) is inscribed in a square of area 24 square units as shown in the figure where four of the vertices are mid points of the sides of the

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A regular polygon with 12 sides (dodecagon) is inscribed in a square of area 24 square units as shown in the figure where four of the vertices are mid points of the sides of the square . The area of the dodecagon in square units is. ans-19.26

Asked In TCS edwin (5 years ago)

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neetu gerwal  (4 years ago)

please provide correct solution

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vamsi  (5 years ago)

Given that the polygon is inscribed inside a square, we can get the sides of the square.
Area = 24 square units.
Side = √24 = 4.899 units
Given that the four vertices of the polygon are the midpoint of the sides, the polygon is divided into four right-angled triangles whose height and base are equal.
The height of each triangle is half the sides of the square.
Therefore:
h = b = 4.899/2
= 2.449
Area of one right angled triangle:
0.5 × 2.449 × 2.449 = 2.9988 square units.
We have four right-angled triangles in the polygon hence the area of the polygon is:
2.9988 × 4 = 11.995 square units

Is this solution Helpfull? Yes (3) | No (15)  

Subhasree Das  (5 years ago)

Given that the the polygon is inscribed inside a square, we can get the sides of the square.

Area = 24 square units.

Side = √24 = 4.899 units

Given that the four vertices of the polygon are the midpoint of the sides, the polygon is divided into four right angled triangle whose height and base are equal.

The height of each triangle is half the sides of the square.

Therefore :

h = b = 4.899/2

= 2.449

Area of one right angled triangle :

0.5 × 2.449 × 2.449 = 2.9988 square units.

We have four right angled triangles in the polygon hence the area of the polygon is :

2.9988 × 4 = 11.995 square units

Is this solution Helpfull? Yes (2) | No (9)  

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