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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.

Sagot :

Rider21idn
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
                                     = 1.68²
                             Area = 2.82 square units   ANSWER