The area of the white square is 64 square units. The diagonal of the square was extended to point A until the length of segment AB was double the length of the diagonal of the square. What is the area of the gray part?

Area of the gray region = 64 square units

Step-by-step explanation:

Area of the white square = 64 square units

Length of a side of the given square =

                                                             =

                                                             = 8 units

By Pythagoras theorem,

Length of diagonal DB =

DB =

     =

AD = DB = [Given]

OD = OC =

               = 4√2

Therefore, AO = AD + OD = 8√2 + 4√2

                                           = 12√2

Area of ΔACD = Area of ΔAOC - Area of ΔCOD

                        =

                        =

                        =

                        = 32

Therefore, area of gray part = Area of ΔACD + Area of ΔAED

                                               = 32 + 32

                                               = 64 square units

64 square units

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.