There is a hexagon MNOPQR of side 5cm. Aman and Ridhima divided it into 2 different ways as shown in the above pic⤴⤴.
Find the area of hexagon using both ways
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UnknownDude
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Excuse my sloppy hexagon making skills, I suck at geometrical shapes (and drawing in general).
In the first method, as you can see in the diagram, the hexagon is divided into a rectangle and two triangles.
5 cm of the total 11 cm is occupied by the rectangle. This leaves 6 cm of height for the other two triangles. Since the triangles are equal in area, their heights will be 3 cm each.
The total area = 5×8 + 2×½×3×8 = 40+24 = 64 cm²
In the second method, the hexagon is divided into two equal trapeziums. The area of a trapezium is ½(a+b)h where a and b are the lengths of the parallel sides and h is the distance between the parallel sides.
The area will be 2×½(5+11)×4 = 16×4 = 64 cm²
Ask me any doubts in da comments.
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UnknownDude
Unless you're extraordinarily talented, I think that's an actual picture
Answers & Comments
Here's your answer...
Excuse my sloppy hexagon making skills, I suck at geometrical shapes (and drawing in general).
In the first method, as you can see in the diagram, the hexagon is divided into a rectangle and two triangles.
5 cm of the total 11 cm is occupied by the rectangle. This leaves 6 cm of height for the other two triangles. Since the triangles are equal in area, their heights will be 3 cm each.
The total area = 5×8 + 2×½×3×8
= 40+24
= 64 cm²
In the second method, the hexagon is divided into two equal trapeziums.
The area of a trapezium is ½(a+b)h where a and b are the lengths of the parallel sides and h is the distance between the parallel sides.
The area will be 2×½(5+11)×4
= 16×4
= 64 cm²
Ask me any doubts in da comments.
[0110100101]...More questions detected... [010110011110]
//Bot UnknownDude is moving on to more queries
//This is your friendly neighbourhood UnknownDude