Question

2. If a square and a rhombus stand on the same base, then find the ratio of the areas of the
and the rhombus.​

Answer 1

Answer:

Consider a square and rhombus standing on the same base 'a'. All the sides of a square are of equal length. Similarly all the sides of a rhombus are also of equal length. Since both the square and rhombus stands on the same base 'a',

Length of each side of the square = a

Length of each side of the rhombus = a

Area of the sqaure = a2 ...(1)

From the diagram, sin θ = ha

=> h = a sin θ

Area of the rhombus = ah = a × a sin θ = a2 sin θ ...(2)

From (1) and (2)

Area of the squareArea of the rhombus=a2a2sinθ=1sinθ

Since 0° < θ < 90°, 0 < sin θ < 1. Therefore, area of the square is greater than that of rhombus, provided both stands on same base.