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In the given figure, ABC is a triangle in which AD and DE are medians to BC and AB respectively, the ratio of the area of BED to that of ABC is:
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Important Questions on Geometry and Mensuration

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Two identical circles intersect so that their centres, and the points at which they intersect, form a square of side 1 cm. The area in square cm of the portion that is common to the two circles is: 
 
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If the height of a cone is trebled and its base diameter is doubled, then the ratio of the volume of the resultant cone to that of the original cone is:
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If two cylinders of equal volume have their heights in the ratio 2:3, then the ratio of their radii is: 
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The area of the rectangle ABCD is 2 and BD=DE. Find the area of the shaded region.
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In a right-angled triangle, the square of the hypotenuse is equal to twice the product of the other two sides. The acute angles of the triangle are: 
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If the sides of a triangle are in the ratio of 12 : 13 : 14, the perimeter is 52 cm, then the length of the smallest side is: