Answer to Question #95410 in Geometry for Subhasis Padhy

Question

If a square and a rhombus stands on same base, then find the ratio between area of square and rhombus ? (For class 9)

Answer 1

Area of square: $S_1=a^2$

Area of rhombus: $S_2=a^2\sin\alpha$, where $\alpha$ is a smaller angle of the rhombus.

$$\frac{S_1}{S_2}=\frac{a^2}{a^2\sin\alpha}=\frac{1}{\sin\alpha}$$

Answer:

$$\frac{1}{\sin\alpha}$$