CAT Question Bank  Geometry (Area)

Q6) ABCD is a square with an area of 8 square meters. A circle is drawn in such a way that the center of the circle lies on the point A and its circumference goes through the midpoint of AB, P and the midpoint of AD. Find the area of the segment that belongs to both the circle and the square.

Q7) Find the maximum area possible for a rectangle, square and a triangle inside a semicircle of radius 6.

Q8) What is the largest possible area of an isosceles triangle with two sides having a length of 2 units?

Q9) If a square and a rhombus stand on the same base , then the ratio of the areas of the square and the rhombus is
A. graater than 1
B. equal to 1
C. equal to 1/2
D. equal to 1/4

Q10) A circular tabletop with maximum possible area is to be cut from a square piece of wood. What percent of the wood surface is not to be used for the tabletop?
a. 21%
b. 25%
c. 35%
d. 30%
e. 18%

Q11) In a triangle ABC, points D and E are on the sides AB and AC such that AD:DC = 1:2 and AE:EC = 3:4. If area of the triangle ABC is 21 units and F is the intersection point of BE and CD then what is the absolute difference between the area of the polygons ADFE and BFC?

Q12) A square is inscribed inside a circle of radius 15. Find the area of the unoccupied region?

Q13) A path 4m broad going through a square shape field, the area of the path is 96 sq m, what's the area of field excluding path?

Q14) A square ABCD, with side = 3cm is rotated by 45 degree (keeping its center fixed) to result into another square PQRS. What is the area of the region common to the squares ?

Q15) If a right isosceles triangle is inscribed in a semi circle, what is the ratio of the area of the circle to the area of the triangle?

Q16) How many rectangles are possible such that its area is five times the perimeter

Q17) The product of the lengths of three sides of a triangle is 196 and the radius of its circumscribe is 2.5 cm. What is the area of the triangle ?

Q18) If ABC is a triangle such that AB = 3cm, BC = 4cm & CA = 5 cm, then area of the largest square in side the triangle ABC is how much % more or less than the area of largest rectangle in side triangle ABC.
a. 0
b. 2.083
c. 2.041
d. None of the above

Q19) Four lines parallel to the base of a triangle divide each of the other sides into five equal segments and the area into five distinct parts. If the area of the largest of these parts is 27, then what is the area of the original triangle ?

Q20) Inside a square ABCD, a point P is selected such that AP = 3, BP = 2, CP = 1. Find the area of ABCD

Q21) A right circular cone of base radius 4cm and height 10cm has a cylinder placed inside it with one of the flat surface resting on the base of the cone . The largest possible area if total surface area of the cylinder is
a. 100π/3
b. 80π/3
c. 120π/3
d. 110π/3

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?