# Let P be a point on the diagonal AC of the square ABCD. If AP is one-fourth of the length of one side of the square and the area of the quadrilateral ABP D is 1 square unit, find the area of ABCD.

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But there are important points we need to understand about a diagonal of a square..

You then can use the formula of area of a triangle A = ab x sinФ..a and b are sides of the triangle.

For triangle ABP, the area is:

A = ab x sinФ

= (x)(x/4) x sin45

A = (x²/4) x (0.707)

But since area of quadrilateral ABPD is 1 square unit, it follows that the area of triangles ABP and ABD are each 1/2 square units..

So we will have:

1/2 = (x²/4) x (0.707)

2 = 0.707x²

Now we got the length of each side of the square ABCD which is 1.68.

Area of the square ABCD = x²

= 1.68²