Question

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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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❄ Explanation required ❄

Answer 1

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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.

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