Geometry questions are not that frequent in placement exams. But questions on mensuration do appear!
1.A square is drawn by joining the midpoints of the sides of a given square. A third square is drawn inside the second square in the same way and this process is continued indefinitely. If a side of the first square is 8 cm, the sum of the areas of all the squares such formed (in sq.cm.)is (a) 128 (b) 120 (c) 96 (d) None of these
2. Let the consecutive vertices of a square S be A,B,C &D. Let E,F & G be the mid-points of the sides B, BC & AD respectively of the square. Then the ratio of the area of the quadrilateral EFDG to that of the square S is nearest to (a) ½ (b) 1/3 (c) ¼ (d) 1/8
Ans – The side of every inner square will be 1/√2 times the side of the outer square. Hence the area of every inner square will be ½ the area of the outer square. The area of the outermost square = 64 sq. cm. So the area of the 2nd square woluld be 32 sq.cm., the 3rd square would be 16 sq.cm. and so on. Hence the sum of all these areas would be : 64 + 32 + 16 + 8 + 4 + ……. This forms a GP with a = 64 and r = ½. It is also a infinitely diminishing series. Hence the sum of all terms = a/(1 – r) = 64/(1 – ½) = 128 sq. cm.
Level of difficulty:- Moderate Expected time to solve:- 10 to 12 minutes.
Hope you learnt!
Happy learning! Gajendra Sir