CAT Question Bank  Geometry (Area)

Q22) Consider a rectangle ABCD of area 90 units. The points P and Q trisect AB, and R bisects CD. The diagonal AC intersects the line segnients PR and QR at M and N respectively. What is the area (A) of the quadrilateral PQMN?
a) 9.5 < A ≤ 10
b) 10 < A ≤ 10.5
c) 10.5 < A ≤ 11
d) 11 < A ≤ 11.5
e) A > 11.5

Q23) Two of the vertices of the regular pentagon drawn on the coordinate plane are known to be (10,20) and (17,40). What is the ratio of the maximum possible area to the minimum possible area of such a pentagon?
(Cos 36 = (√5 + 1)/4)
a. 4  (√5/2)
b. 2 + (√5/2)
c. (3 +√5)/2
d. 3 + (2/√5)

Q24) Let VK and KJ be perpendicular line segments, each of which of length 6 cm. Suppose P and Q are the midpoints of VK and KJ respectively. If R is the point of intersection of VQ and PJ, then the area of triangle RQJ is
a) 6 sq. cm
b) 3 sq. cm
c) 3√2 sq. cm
d) 6√2 sq. cm

Q25) A triangle has vertex A at (0, 3), vertex B at (4, 0), and a vertex C at (x, 5) for some x where 0 < x < 4. If the area of the triangle is 8, what is the value of x?

Q26) Mandakini draws a square ABCD of side 1 unit. She then draws 10 straight lines connecting A to each of 11 equally spaced points lying internally on CD (including C and D). What is the total area (in unit square) of all the possible triangles that can be formed

Q27) If the sum of the lengths of three sides of a rectangle is 100 units, then find the maximum possible area of the rectangle ?

Q28) 2 circles of radii r and 2r intersect each other in such a way that their common chord is of maximum possible length. What is the area of region common to both?

Q29) The midpoints of 4 sides of a regular hexagon are joined to form a rectangle. Ratio of the area of rectangle to hexagon is

Q30) Two different triangles with side lengths 18, 24, and 30 are given such that their incircles coincide and their circumcircles coincide. What is the area of the polygon that the triangles have in common?
