Chapter-11 (Mensuration-Areas related tol circle)

1 .Area of a triangle with sides 3cm, 4cm, 5cm is ____

a)6√2sqcm

b)2sqcm

c)3sqcm

d) 41sqcm

2. Area of a right triangle whose perpendicular sides are 15cm, 10cm is

a) 2

b)75sq cm

c) 54sq cm

d) 34sq cm.

3. Perimeter of a right triangle with base 3cm and hypotenuse 5cm is

a)11cm

b) 13cm

c) 12cm

d)14cm.

4. Area of an isosceles right triangle having one of the equal sides 4cm is a) 3sq cm

b) 4sqcm

c) 5sq cm

d) 8sq cm

5. Area of an equilateral triangle of side 6cm is _______

a)4√3sq cm

b)3sq cm

c)4sq cm

d)5sq cm.

6 .If the area of an equilateral triangle is 25√3sq cm, then its side is

a)8cm

b)10cm

c)9cm

d)12cm.

7 Perimeter of a rectangle of sides 7cm and 3cm is _________

1. 18cm
2. b)32cm
3. c)20cm
4. 23cm

8 Area of a rectangle with dimensions 5cm, 4cm is _________

a)54cm

b)21sq cm

c) 13sq cm

d)20sq cm

9. Area of a square with side 8cm is ____

1. 64sqcm
2. 34sqcm
3. 43sqcm

d ) 12sqcm

10. Perimeter of a square is 14cm. Find the side.

a)3cm

b)3.5cm

c)4cm

d)5cm

11. Find the area of a parallelogram with altitude 4cm, base 5cm.

1. 54sqcm
2. 12sqcm
3. 20sqcm
4. 23sqcm

12. Calculate the perimeter of a parallelogram with dimensions 12cm and 15cm.

a) 43cm

b) 23sqcm

c) 65cm

d) 54cm

13.Area of a rhombus whose diagonals are 11cm, 12cm.

a)66sqcm

b)34sqcm

c)35sqcm

d)53sqcm

14. Determine the area of a trapezium with parallel sides 6cm,7cm and height 5cm.

a)21sqcm

b)32.5sqcm

c)67sqcm

d)12.8sqcm

15. Workout the area of a quadrilateral with diagonal 7cm and altitudes on the diagonal are 3cm, 4cm.

a)42.3sqcm

b)21sqcm

c)24.5sqcm

d)19sqcm

16.Determine the area of a regular hexagon of side 4cm.

a)34sqcm

b)32sqcm

c)23sqcm

d)41.57sqcm

17. The length and breadth of a rectangular hall are 24m, 12. Carpets of size 8mx4m are available. How many carpets are needed to cover the hall?

a)9

b)4

c)2

d)10

18. A sector is cut from a circle of radius 28cm. The angle of the sector is 120degrees.Find the length of its arc. a)32.1cm

b)58.67cm

c)23cm

d)12cm

19. Find the area of a pathway which is in the shape of a ring with outer circumference 406m and inner circumference370m

a)43sqcm

b)2sqcm

c)2222.25sqcm

d)9sqcm

20. Find the area of sector of a circle of radius 42cm with central angle 90degrees.

a)231sqcm

b)213sqcm

c)1234sqcm

d)1386sqcm

21. The minute hand of a clock is 11cm long. Find the area swept by it between 8.30pm and 8.40pm.

a)63.4sqcm

b)124sqcm

c)65sqcm

d)34sqcm

22. The side of a regular pentagon is 12cm. Find its area.

a)45sqcm

b)180√3sqcm

c)38sqcm

d)24sqcm

23. A chord PQ of a circle of radius 7cm makes an angle of 30degrees at the centre. Find the area of the major segment.

a)56sqcm

b)12sqcm

c)153.41sqcm

d)9sqcm

24. Volume of a cube of side 7.1cm is__________

a)32sqcm

b)21sqcm

c)46sqcm

d)357.91sqcm

25. Volume of a cuboid of dimensions 3cm,4cm, 5.2cm is ________

a)6.24sqcm

b)32.1sqcm

c)34sqcm

d)21sqcm

SOLUTIONS:

1. Area of a scalene triangle is √s(s-a)(s-b)(s-c) sq units, where s is the semi perimeter.

S= (a+b+c)/2 = (3+4+5)/2 = 12/2 =6, Area =√6(6-3)(6-4)(6-5)=√6x3x2x1=√36=6sqcm

2. Area of the right angled triangle = 1/2x15x10 = 75sq cm. (area = 1/2x product of perpendicular sides).

3. Given hypotenuse and one side. Hence the other side = √5²-3² = √25-9 = √16 = 4

Perimeter = 3+4+5 = 12cm.

4. Area of an isosceles right triangle having one of the equal sides as 4cm = ½ x a²

Area = ½ x 4x4 = 8sq cm.

5. Area of an equilateral triangle with side 6cm = √3/4 x a² = √3/4 x 6x6 = 9√3sq cm.

6. Given area of the equilateral triangle √3/4 x a² = 25√3 => a²/4 = 25 => a²=100=>a=10cm.

7. Perimeter of a rectangle of sides 7cm and 3cm is = 2(l+b) = 2(7+3) = 2(10) = 20cm.

8. Area of a rectangle of sides 5cm and 4cm = lxb = 5x4 = 20sq cm.

9. Area of a square of side 8cm =sidexside = 8x8 = 64sq cm.

10. Given perimeter of the square 14cm. => 4a = 14=>a = 14/4 = 3.5cm.

11. Area of a parallelogram = axh = base x height = 5x4 = 20sq cm.

12. Perimeter of a parallelogram with dimensions = 2(a+b) = 2(12+15) 2(27) = 54cm.

13. Area of a rhombus whose diagonals are d1 = 11cm, d2 = 12cm is = ½ *d1*d2

Area = ½ *11*12 = 66sq cm.

14. Area of a trapezium with parallel sides 6cm and 7cm and height 5cm is = ½(a+b)h

Area = ½(6+7)*5 = ½*13*5 = 65/2 = 32.5sq cm.

15. Area of a quadrilateral = ½*AC*(h1+h2) = ½*7*(3+4) = 49/2 = 24.5sq cm.

16. Area of regular hexagon of side 4cm = 3√3/2*a² = 3√3/2*4*4 = 24√3sqcm.

17. Number of carpets needed = Area of hall/area of carpet. = 24 x 12/8 x 4 = 9carpets.

18. Length of arc of a sector = Q/360 * 2Пr = 120/360 * 2 *22/7*28 = 176/3 = 58.67cm.

19. Area of a pathway in the form of ring = П(R+r)(R-r)

Outer circumference = 406m => 2ПR = 406=>R = 406/2П Inner circumference = 2Пr = 370 = r = 370/2П. Area =П(406/2П+370/2П)(406/2П-370/2П) =>П/4П²(776) (36)

• 1/П (776) (9) => 7/22(776) (9) = 2222.18sq cm.

20. Area of a sector = Q/360 *Пr² = 90/360*22/7*42*42 = 1386sq cm.

21. Length of the minute hand = r = 11cm. Angle subtended by the minute hand

Between 8.30am and 8.40am = 60degrees. (Angle subtended by the minute hand in 60min =360degrees, angle subtended in 10minutes = 10*360/60 = 60degrees.)

Area swept by the minute hand = area of the sector = 60/360*22/7*11*11 = 63.4sq cm.

22. Side of a pentagon = 12cm Area = 5*√3/4*a² = 5*√3/4*12*12 = 180√3 sq cm.

23. Area of major segment = Area of circle-Area of minor segment.

= Пr²- (Q/360Пr²-1/2r²sinQ)

=22/7*7*7 – (30/360*22/7*7*7-1/2*7*7*1/2) ( as sin30 = ½)

=22*7 – (1/12*22*7-1/4*7*7)

154-7/12 = 1841/12 = 153.41sq cm.

24. Volume of a cube = a³ = 7.1*7.1*7.1 = 357.91cubic cm.

25. Volume of a cuboid = l*b*h = 3x4x5.2 = 6.24cu cm.