12. If a square and a rhombus stand on the same base, then what is the ratio of the areas of the square and the rhombus? | |

A. equal to ½ | B. equal to ¾ |

C. greater than 1 | D. equal to 1 |

Here is the answer and explanation

Answer : Option D

Explanation :

**Hence ratio of the areas of the square and the rhombus will be equal to 1 since
they stand on the same base**

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Note : Please find the proof of the formula given below which you may like to go through

Let ABCD be the square and ABEF be the rhombus

Consider the right-angled triangles ADF and BCE

We know that AD = BC (∵ sides of a square)

AF = BE (∵ sides of a rhombus)

∵ DF = CE [∵ DF

^{2}= AF

^{2}- AD

^{2}and CE

^{2}= BE

^{2}- BC

^{2}]

Hence Δ ADF = Δ BCE

=> Δ ADF + Trapezium ABCF= Δ BCE + Trapezium ABCF

=> Area of square ABCD = Area of rhombus ABEF

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