I cant draw the figure here. Lets let the sides of the square be "x"
But there are important points we need to understand about a diagonal of a square..A diagonal of a square bisects the square into to equal triangles. Hence the 90° angle is also bisected into two 45° angles..
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
1.68 = x
Now we got the length of each side of the square ABCD which is 1.68.
Area of the square ABCD = x²
Area = 2.82 square units ANSWER