QUADRILATERAL AND POLYGON (CDS)

Total Questions: 41

1. The sides AD BC , of a trapezium ABCD are parallel and the diagonals AC and BD meet at O. If the area of triangle AOB is 3 cm² and the area of triangle BDC is 8 cm² , then what is the area of triangle AOD? [2019 (II) Evening Shift]

Correct Answer: (d) 8 cm²
Solution:



2. Let PQRS be a parallelogram whose diagonals PR and QS intersect at O. If triangle QRS is an equilateral triangle having a side of length 10 cm, then what is the length of the diagonal PR? [2019 (II) Evening Shift]

Correct Answer: (a) 5√3 cm
Solution:


3. The corners of a square of side ‘a’ are cut away so as to form a regular octagon. What is the side of the octagon? [2019 (I) Morning Shift]

Correct Answer: (a)
Solution:



4. Consider the following statements: [2019 (I) Morning Shift]

1. An isosceles trapezium is always cyclic.
2. Any cyclic parallelogram is a rectangle.

Which of the above statements is/are correct?

Correct Answer: (c) Both 1 and 2
Solution:



5. In the figure given below, ABC is an equilateral triangle with each side of length 30 cm. XY is parallel to BC, XP is parallel to AC and YQ is parallel to AB. If XY + XP + YQ is 40 cm, then the value of PQ is [2018 (II) Evening Shift]

Correct Answer: (d) 10 cm
Solution:

6. Given, that the angles of a polygon are all equal and each angle is a right angle. [2018 (I) Morning Shift]

Statement 1 : The polygon has exactly four sides.
Statement 2 : The sum of the angles of a polygon having n sides is (3n - 8) right angles.

Which one of the following is correct in respect of the above statements?

Correct Answer: (c) Statement 1 is true, but statement 2 is false.
Solution:Statement 1 is true, but Statement 2 is false as the sum of angle of polygon is (n − 2) 180° .

7. If a point O in the interior of a rectangle ABCD is joined with each of the vertices A B, C and D, then OB² + OD² will be equal to [2017 (II) Evening Shift]

Correct Answer: (c) OC² + OA²
Solution:We have ABCD is rectangle

8. A closed polygon has six sides and one of its angles is 30° greater than each of the other five equal angles. What is the value of one of the equal angles? [2017 (II) Evening Shift]

Correct Answer: (b) 115°
Solution:We know that, if a polygon has n sides, then the sum of its interior angles is given by (n − 2) 180°

9. Let ABCD be a rectangle. Let P, Q, R, S be the mid-points of sides AB, BC, CD, DA respectively. Then the quadrilateral PQRS is a [2017 (I) Morning Shift]

Correct Answer: (c) Rhombus, but need not be a square
Solution:



10. The area of a regular hexagon of side ‘a’ is equal to [2017 (I) Morning Shift]

Correct Answer: (b)
Solution: