# Geometry basics

Dear students,

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

**Solution :-**

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.

**Analysis**

**Level of difficulty:- Moderate **
**Expected time to solve:- 10 to 12 minutes.**

Hope you learnt!

Happy learning! Gajendra Sir

Trainer, eXtraSem