CAT 1991 — QA Question 19
Basics of QuadrilateralsEasy
Let the consecutive vertices of a square S be A, B, C & D. Let E, F & G be the mid-points of the sides AB, 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
Answer & solution
Correct answer: 1/2
1/2
- B
1/3
- C
1/4
- D
1/8
Solution
Let the side of square be a.
Area of quadrilateral EFDG = Ar(â³DGF) + Ar(â³GEF) = 1/2 × a/2 × a + 1/2 × a × a/2 = 1/2 × a2
Ar(EFDG) : Ar(S) = 1/2 × a2 : a2 = 1 : 2
Hence, option (a).