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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 :

A square and a rhombus on the same base will have equal areas.

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

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 [? DF2 = AF2 - AD2 and CE2 = BE2 - BC2]

Hence ? ADF = ? BCE

=> ? ADF + Trapezium ABCF= ? BCE + Trapezium ABCF

=> Area of square ABCD = Area of rhombus ABEF


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