 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that the given diamond kite is square shaped. If the straight line from one end of the kite to the opposite end is 127 cm long, find the area of the kite we know that Pythagorean theorem states sum of squares of the length of a right angle triangle is equal to the square of the length of the hypotenuse that is in a right angle triangle with hypotenuse c and sites a and b we have c square is equal to a square plus b square with this key idea we shall move on to the solution. In this question we are given a square shaped kite such that the straight line from one end to the opposite end of the kite is 127 cm long and we have to find the area of the kite. Now we know that area of square is equal to site square so to find the area of kite we first need to find the length of its site since it is a square so all the angles measure will be 90 degrees and length of all sites is equal. Now let us label this end b l opposite end b m and this end of the kite b p then triangle l m p is a right angle triangle right angle that p so site l m will be the hypotenuse of triangle l m p and l p and p m will be the other two sites of the triangle since it is a square so length of site l p will be equal to length of site p m so in right angles triangle l m p l m is equal to 127 cm and let l p which is equal to p m be equal to x cm Now using Pythagoras theorem in right angle triangle l m p we have l p square plus p m square is equal to l m square that is l p that is equal to x so l p square will be x square plus p m square that is also x square is equal to l m square that is 127 square this implies x square plus x square is 2x square which is equal to 127 square that is 16129 which further implies that x square is equal to 16129 upon 2 which implies that x square is equal to 8064.5 by rounding of this number we get x square is approximately equal to 8065 now we know that area of kite is equal to site square which will be equal to x square and we know that x square is approximately equal to 8065 so this is approximately equal to 8065 thus the area of the kite is 8065 square cm approximately this is the required answer this completes our session hope you enjoyed this session