CBSE Class 9 Mathematics Areas Of Parallelogram And Triangles Worksheet Set A

Question. Two opposite angles of a parallelogram are \( (3x - 2)^\circ \) and \( (50 - x)^\circ \). Find the measure of each angle of the parallelogram.
Answer: \( 37^\circ, 143^\circ, 37^\circ, 143^\circ \)

Question. If an angle of a parallelogram is two-third of its adjacent angle, find the angles of the parallelogram.
Answer: \( 108^\circ, 72^\circ, 108^\circ, 72^\circ \)

Question. Find the measure of all the angles of a parallelogram, if one angle is \( 24^\circ \) less than twice the smallest angle.
Answer: \( 68^\circ, 112^\circ, 68^\circ, 112^\circ \)

Question. The perimeter of a parallelogram is 22 cm. If the longer side measures 6.5 cm what is the measure of the shorter side?
Answer: 4.45 cm

Question. In a parallelogram ABCD, \( \angle D = 135^\circ \), determine the measures of \( \angle A \) and \( \angle B \).
Answer: \( \angle A = 45^\circ, \angle B = 135^\circ \)

Question. If one angle of a parallelogram is \( 24^\circ \) less than twice the smallest angle, then find the largest angle of the parallelogram.
Answer: \( 112^\circ \)

Question. If an angle of a parallelogram is two-third of its adjacent angle, then find smallest angle of the parallelogram.
Answer: \( 72^\circ \)

Question. Two parallelograms stand on equal bases and between the same parallels. Then find ratio of their areas.
Answer: 1 : 1

Question. If a rectangle and a parallelogram are equal in area and have the same base and are situated on the same side, then the quotient: \( \frac{\text{Perimeter of rectangle}}{\text{Perimeter of || gm}} \)
Answer: Less than 1

Question. ABCD is a parallelogram, E, F are the mid points of BC and AD respectively and G is any point on EF. Then find area of \( \Delta GAB \).
Answer: \( \frac{1}{4} (\text{||gm ABCD}) \)

Question. The altitude of a parallelogram is twice the length of the base and its area is 1250 \( cm^2 \). Then find lengths of the base and the altitude.
Answer: 25 cm, 50 cm

Question. If the ratio of the altitude and the area of the parallelogram is 2 : 11, then find the length of the base of the parallelogram.
Answer: 5.5 units

Question. Two adjacent sides of a parallelogram are 24 cm and 18 cm. If the distance between the longer sides is 12 cm, then find the distance between the shorter sides.
Answer: 16 cm

Question. The area of a triangle is equal to the area of a rectangle whose length and breadth are 18 cm and 12 cm respectively. If the base of the triangle is 24 cm, then find its altitude.
Answer: 18 cm

True/False Type Questions

Question. In a parallelogram, the diagonals are equal.
Answer: False

Question. In a parallelogram, the diagonals bisect each other.
Answer: True

Question. In a parallelogram, the diagonals intersect each other at right angles.
Answer: False

Question. If ABCD is a parallelogram with two adjacent angles A and B equal to each other, then the parallelogram is a rectangle.
Answer: True

Question. If ABCD is a parallelogram and E, F are the centroids of \( \Delta s \) ABD and BCD respectively, then EF = AE.
Answer: True

Question. ABCD is a parallelogram one of whose diagonals is AC. Then \( ar (\Delta ADC) = ar (\Delta CBA) \)
Answer: True

Fill in the blanks Types Questions

Question. The triangle formed by joining the mid points of the sides of an isosceles triangle is ……… .
Answer: Also isosceles \( \Delta \)

Question. The triangle formed by joining the mid points of the sides of a right triangle is ……….. .
Answer: Also right angle \( \Delta \)

Question. The figure formed by joining the mid points of the consecutive sides of a quadrilateral is ……
Answer: Parallelogram

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