Sloping Square

Geometry Level 2

In a big square of side length 5cm, ABCD, A is joined to the midpoint of BD, B is joined to the midpoint of CD, C is joined to the midpoint of AB, and D is joined to the midpoint of AC. Find the area, in cm², of the yellow shaded square formed by this construction.


The answer is 5.

Tan Chee Sen by Tan Chee Sen , 25, Malaysia

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2 solutions

Chetana Sudhir
Jul 20, 2014

Its the easiest problem, actually. With all the info given, one can figure that the dia is actually made up of 5 congruent smaller squares,including the yellow one. So, area = (5 cm * 5 cm)/5 squares = 5cm².

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Rohit Sachdeva
Aug 26, 2014

Since i cannot add a figure, i will try & explain:

Let mid pt of BD be P, and AMNP be the straight line such that MN is the side of yellow square (=s)

We can see by mid-pt theorem or elseways that AM=MN (=s)

Hence BN=s by symmetry

Area of ANB=(1/2)xsx2s=s²= Area of square

Hence big square contains 4 triangle and a yellow square each of area s²

Hence area of yellow square =5²/5=5

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