Class 9 Practice – Level 2 – Set 2 – Quadrilaterals

Total questions: 25

Find the area of a trapezium whose parallel sides are 11m and 25m long, and the nonparallel sides are 15m and 13m long.

Topic: Area of a Trapezium

$ \displaystyle 216{{m}^{2}}$

$ \displaystyle 336{{m}^{2}}$

$ \displaystyle 358{{m}^{2}}$

$ \displaystyle 458{{m}^{2}}$

None

Find the perimeter and area of a quadrilateral ABCD in which BC = 12 cm, CD = 9 cm, BD = 15cm, DA= 17 cm and ∠ ABD = 90°.

Topic: Perimeter and Area of a Quadrilateral

$ \displaystyle 548c{{m}^{2}}$

$ \displaystyle 105c{{m}^{2}}$

$ \displaystyle 123c{{m}^{2}}$

$ \displaystyle 114c{{m}^{2}}$

None

ABCD is a trapezium in which AB∥DC and P,Q are the midpoints of AD and BC respectively. DQ and AB when produced to meed at E. Also, AC and PQ intersect at R. then the AR = RC

Topic: Properties of Trapezium

True

False

Sometimes True

None of the above

None

M and N are points on opposite sides AD and BC of a parallelogram ABCD such that MN passes through the point of intersection O of its diagonals AC and BD. Then the MN is bisected at O.

Topic: Properties of a Parallelogram

Yes

Sometimes yes

None of the above

None

ABCD is a trapezium in which AB∥DC and P,Q are the midpoints of AD and BC respectively. DQ and AB when produced to meed at E. Also, AC and PQ intersect at R. then the PR ∥ AB

Topic: Properties of Trapezium

True

False

None

The height of an equilateral triangle measures 9cm. Find its area, correct upto 2 places of decimal. Take $ \displaystyle \sqrt{3}$=1.732

Topic: Area of an Equilateral Triangle

78.509$ \displaystyle c{{m}^{2}}$

36.255$ \displaystyle c{{m}^{2}}$

46.764$ \displaystyle c{{m}^{2}}$

25.369$ \displaystyle c{{m}^{2}}$

None

The sides of a quadrilateral ABCD taken in order are 6cm, 8cm, 12 cm and 14cm respectively and the angle between the first two sides is a right angle. Find its area. (Given, $ \displaystyle \sqrt{6}$= 2.45.)

Topic: Angles of a Quadrilateral

$ \displaystyle 75.3c{{m}^{2}}$

$ \displaystyle 66.9c{{m}^{2}}$

$ \displaystyle 82.8c{{m}^{2}}$

$ \displaystyle 45.2c{{m}^{2}}$

None

The area of a trapezium is 475$ \displaystyle c{{m}^{2}}$ and its height is 19cm. Find the lengths of its two parallel sides if one side is 4cm greater than the other.

Topic: Area of a Trapezium

23cm, 27cm

65cm, 12 cm

14cm, 63 cm

28cm, 45cm

None

The difference between the semiperimeter and the sides of a ΔABC are 8cm, 7cm and 5cm respectively.Find the area of the triangle.

Topic: Area of a Triangle

$ \displaystyle 24\sqrt{{14}}$

$ \displaystyle 20\sqrt{{14}}$

$ \displaystyle 30\sqrt{{14}}$

$ \displaystyle 50\sqrt{{14}}$

None

10.

The difference between the lengths of the parallel sides of a trapezium is 8cm, the perpendicular distance between these sides is 24cm and the area of the trapezium is $ \displaystyle 312c{{m}^{2}}$. Find the length of each of the parallel sides.

Topic: Area of a Trapezium

2cm, 18cm

8cm, 10cm

9cm, 17cm

5cm, 9cm

None

11.

The perimeter of a triangle is 50cm. One side of the triangle is 4cm longer than the smaller side and the third side is 6cm less than twice the smaller side. Find the area of the triangle.

Topic: Area of a Triangle

$ \displaystyle 55\sqrt{{45}}c{{m}^{2}}$

$ \displaystyle 20\sqrt{{30}}c{{m}^{2}}$

$ \displaystyle 40\sqrt{{10}}c{{m}^{2}}$

$ \displaystyle 10\sqrt{{15}}c{{m}^{2}}$

None

12.

A parallelogram and a rhombus are equal in area. The diagonals of the rhombus measure 120m and 44m. If one of the sides of the parallelogram measures 66m, find its corresponding altitude.

Topic: Area of Parallelogram and Rhombus

10m

40m

30m

20m

None

13.

A floral design on a floor is made up of 16 tiles, each triangular in shape having sides 16cm, 12cm and 20cm. Find the cost of polishing the tiles at 1 per sq cm.

Topic: Area of a Triangle

₹1396

₹1458

₹1025

₹1536

None

14.

The base of a triangular field is three times its altitude. If the cost of sowing the field at Rs. 58 per hectare is Rs. 783, find its base and height.

Topic: Area of a Triangle

300m

900m

700m

500m

None

15.

The sides of a triangle are in the ratio 5 : 12 : 13, and its perimeter is 150 m. Find the area of the triangle.

Topic: Area of a Triangle

175

750

350

150

None

16.

If the area of an equilateral triangle is $ \displaystyle 81\sqrt{3}c{{m}^{2}}$, then what is the value of its height.

Topic: Area of an Equilateral Triangle

94cm

36cm

42cm

68cm

None

17.

A rhombus-shaped sheet with perimeter 40cm and one diagonal 12cm, is painted on both sides at the rate of 5 per$ \displaystyle c{{m}^{2}}$. Find the cost of painting.

Topic: Angles in a Rhombus

₹520

₹960

₹850

₹658

None

18.

A parallelogram and a square have the same area. If the sides of the square measure 40m and altitude of the parallelogram measures 25m, find the length of the corresponding base of the parallelogram.

Topic: Angles in a Parallelogram

64m

35m

26m

45m

None

19.

Find the area of the triangle whose base measures 24 cm and the corresponding height measures 14.5 cm.

Topic: Area of a Triangle

136

146

174

158

None

20.

A rectangular plot is given for constructing a house, having a measurement of 40m long and 15m in the front. According to the laws, a minimum of 3m wide space should be left in the front and back each and 2m wide space on each of the other sides. Find the largest area where house can be constructed.

Topic: Angles in a Rectangle

$ \displaystyle 145{{m}^{2}}$

$ \displaystyle 789{{m}^{2}}$

$ \displaystyle 374{{m}^{2}}$

$ \displaystyle 546{{m}^{2}}$

None

21.

What is the area of the rhombus one side of which measures 20cm and one of whose diagonals is 24cm.

Topic: Angles in a Rhombus

294

384

574

886

None

22.

A rectangular lawn, 75m by 60m, has two roads, each road 4m wide, running through the middle of the lawn, one parallel to length and the other parallel to breadth, as shown in the figure. Find the cost of gravelling the roads at 50 per $ \displaystyle {{m}^{2}}$.

Topic: Angles in a Rectangle

₹45823

₹26200

₹25460

₹32568

None

23.

In quadrilateral ABCD,AP and BP are bisectors of ∠A and ∠B respectively, then the value of x is :

Topic: Angle Bisectors in Quadrilaterals

60°

180°

90°

95°

None

24.

In the given figure (not to scale), ABC is an isosceles triangle in which AB=AC. AEDC is a parallelogram. If ∠CDF = 70° and ∠BFE = 100°, then find ∠FBA.

Topic: Properties of Isosceles Triangle and Parallelogram