List of top Quantitative Ability and Data Interpretation Questions on Triangles, Circles & Quadrilaterals

The problem below consists of a question and two statements numbered 1 & 2. You have to decide whether the data provided in the statements are sufficient to answer the question.
In a cricket match, three slip fielders are positioned in a straight line. The distance between the 1st slip and the 2nd slip is the same as the distance between the 2nd slip and the 3rd slip. The player X, who is not on the same line of slip fielders, throws a ball to the 3rd slip and the ball takes 5 seconds to reach the player at the 3rd slip. If he had thrown the ball at the same speed to the 1st slip or to the 2nd slip, it would have taken 3 seconds or 4 seconds, respectively. What is the distance between the 2nd slip and player X?
1. The ball travels at a speed of 3.6 km/hour.
2. The distance between the 1st slip and the 3rd slip is 2 meters.

ABC is a triangle and the coordinates of A, B, and C are (a, b - 2c), (a, b + 4c), and (-2a, 3c), respectively, where a, b, and c are positive numbers. The area of the triangle ABC is:

ABC is a triangle with BC = 5. D is the foot of the perpendicular from A on BC. E is a point on CD such that BE = 3. The value of AB²-AE²+6CD is:

What is the area of an equilateral triangle whose inscribed circle has radius R?

In the following diagram, if the shaded area is one half the area of triangle ABC and angle ABC is right angle then the length of line segment AD is

Given below are two statements:
Statement I : If the roots of a quadratic equation are 2 and 3, then the equation is \(x^2-5x-6=0.\)
Statement II: If the roots of \(4x^2+3kx+9=0\) are real and distinct, then \(k≤-4\) or \(k≥4.\)
In the light of the above statements, choose the most appropriate answer from the options given below:

Which of the following sets of numbers can be used as the lengths of the sides of a triangle?

A square is inscribed in an equilateral triangle such that one of the sides of the square completely lies on one of the sides of the equilateral triangle. Find the ratio of the perimeters of the square and equilateral triangle.