1) The paint in a certain container is sufficient to paint an area equal to 9.375 sq.m. How many bricks of dimensions 22.5 cm × 10 cm × 7.5 cm can be painted out of this container?
2) Prove that the angle bisectors of a parallelogram form a rectangle.
3) Calculate all the angles of a quadrilateral if they are in the ratio 2:5:4:1.
4) Find the area of a triangle whose two sides are 18 cm and 10 cm and the perimeter is 42cm.
5) Two adjacent angles on a straight line are in a ratio of 5:4. Find the measure of each one of these angles.
6) AB and CD are equal chords of a circle whose center is O. When produced, these chords meet at E. Prove that EB = ED.


7) The length, breadth, and height of a room are 5 m, 4 m, and 3 m respectively. Find the cost of whitewashing the walls of the room and the ceiling at the rate of Rs.7.50 per sq.m.
8) In a trapezium ABCD, AB∥CD. Calculate ∠C and ∠D if ∠A = 55° and ∠B = 70°
9) Curved surface area of a right circular cylinder is 4.4 sq.m. If the radius of the base of the cylinder is 0.7 m, find its height.
10) Two chords AB and CD of lengths 5 cm and 11 cm respectively of a circle are parallel to each other and are on opposite sides of its center. If the distance between AB and CD is 6cm, find the radius of the circle.
11) If two intersecting chords of a circle make equal angles with the diameter passing through their point of intersection, prove that the chords are equal.
12) AD and BC are equal perpendiculars to a line segment AB. Show that CD bisects AB.
13) A field is in the shape of a trapezium whose parallel sides are 25 m and 10 m. The non-parallel sides are 14 m and 13 m. Find the area of the field.
Directions:
(a) Assertion and reason are true and the reason is the correct explanation of assertion.
(b) Both assertion and reason are true but the reason is not the correct explanation of assertion.
(c) Assertion is true but the reason is false.
(d) Assertion is false but the reason is true.
14) (i) Assertion: The angles of a quadrilateral are x0, (x – 10)0, (x + 30)0 and (2x)0, the smallest angle is equal to 580.
Reason: The sum of the angles of a quadrilateral is 3600.
(ii) Assertion: In a circle of radius 6 cm, the angle of a sector is 60°.Then the area of the sector is 186/7 cm².
Reason: The area of the circle with radius r is πr²
15) Case study
After summer vacation, Manit’s class teacher organized a small MCQ quiz, based on the properties of quadrilaterals. During quizzes, she asks different questions to students. Some of the questions are listed below.






( I ) Which of the following is/are the condition(s) for ABCD to be a quadrilateral?
. (a) The four points A, B, C, and D must be distinct and co-planar.
. (b) No three of points A, B, C, and D are collinear.
(c) Line segments i.e., AB, BC, CD, DA intersect at their endpoints only.
. (d) All of these
(ii) Which of the following is the wrong condition for a quadrilateral said to be a parallelogram?
(a) Opposite sides are equal
(b) Opposite angles are equal
(c) Diagonal can’t bisect each other
(d) None of these
(iii) If AX and CY are the bisectors of the angles A and C of a parallelogram ABCD, then
(a) AX || CY
(b) AX || CD
(c) AX || AB
(d) None of these
(IV) If angles of a quadrilateral are in ratio 3: 5: 5: 7, then find all the angles.
(a) 54°, 80°, 80°, 146°
(b) 34°, 100°, 100°, 126°
(c) 54°, 90°, 90°, 126°
(d) None of these