Question

a square and rhombus stand on same base ,then the ratio of area of square and rhombus is ??​

Answer 1

greater than 1

Solution

Area of square = a^2 where a is base length

Area of rhombus with same base = a * h where h is perpendicular height. This height can be changed from a to 0 so definitely area on square will be more than area of rhombus.

Answer 2

the area of a quadrilateral is equal to b*h where b is the base and h is the height.

the area of the square is equal to b*b = b^2 because the base and the height of the square are the same.

the area of the rhombus is equal to b*h.

b is equal to the base.

h is equal to the height.

the height of the rhombus depends on the acute angle that the side of the rhombus makes with the base.

this affects the area of the rhombus.

a larger acute angle (90 degrees is the largest) results in a larger area.

this means that the greaer area is when the rhombus is in fact a square.

anything less than that will result in a smaller area.

assuming that the angle is A, then the height of the rhombus is equal to b*sin(A)

where b is the length of a side of the rhombus.

the area of the rhombus is therefore equal to b*b*sin(A) which is equal to b^2*sin(A).

the ratio of the area of the square to the area of the rhombus is equal to:

area of square / area of rhombus = b^2 / b^2*sin(A) is equal to 1/sin(a) which is equal to cosecant(A).

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