area and perimeter

Area and Perimeter

1.          Find the area of a triangle whose sides are 13 cm, 14 cm and 15 cm in length.

(A) 96 cm²                           (B)84 cm²                          (C) 108 cm²                    (D)90 cm²                       (E) None of these

2.          Find area of a right triangle whose base is 12 cm and hypotenuse 13 cm.

(A) 30 cm2                 (B) 60 cm2                (C) 65 cm2                      (D) 78 cm2             (E) None of these

3.          The ratio of the areas of two triangle is 4 : 3 and ratio of their heights is 3 : 4. Find the ratio of their bases.

(A) 16 : 3                    (B) 1 : 1                     (C) 16 : 9                           (D) 9 : 16                 (E) None of these

4.          Area  of  an equilateral triangle is 25 cm² .  Find the side of triangle.

(A) 10 cm                  (B) 7 cm                  (C) 12 cm                          (D) 8 cm                    (E) None of these

5.          The base of a triangle is 15 m and height is 12 m. The area of another triangle is twice the area this triangle and base of second triangle is 20 m. The height of this triangle is

(A) 4.5 m                    (B) 9 m                     (C) 12 m                        (D) 18 m                  (E) None of these

6.          One of the side of a right angled triangle is 9 cm and the area of the triangle is 180 sq.cm. Find the hypotenuse.  

(A) 41 cm                 (B) 42 cm                   (C) 39 cm                     (D) 45 cm (E) None of these

7.          The base of a triangular field is three times its altitude. If the cost of cultivating the field at Rs. 50 per hectare be Rs. 675, then find base.

(A) 300 m                   (B) 900 m                 (C) 450 m                    (D) 150 m                (E) None of these

8.          One side of a rectangular field is 15 m and one of its diagonals is 17 m. Find the area of the field.

(A) 125 m²                (B) 120 m²              (C) 130 m²                  (D) 126 m²             (E) None of these

9.          Perimeter of a rectangle is 56 cm and length is 15 cm. Find the area of rectangle.

(A) 190cm²                (B) 185 cm²            (C) 195 cm²               (D) 200 cm²           (E) None of these

10.      Length and breadth of rectangular field are in the ratio 3 : 2. If perimeter of field is 100 m, then find the length of the field.  

(A) 35 m                     (B) 40 m                 (C) 25 m                   (D) 30 m                       (E) None of thes 

11.      In a rectangle, the breadth is of its length. If the area is 768 m² , then find its breadth.

(A) 24 m                     (B) 30 m                  (C) 34 m                    (D) 25 m                       (E) None of these

12.      The length of a rectangular plot is 20 meter more than its breadth. If the cost of fencing the plot with rate of Rs. 26.50 per meter is Rs. 5300, then what is the length of plot ?

(A) 50 m                     (B) 40 m                (C) 60 m                        (D) 65 m                      (E) None of these

13.      The length and breadth of a rectangle is 35 m and 30 m respectively. How many square beds are possible in this rectangle if the side of bed 5 m.

(A) 40                          (B) 48                   (C) 45                            (D) 42                            (E) None of these

14.      A room, 10m  long and 8 m wide, is to be designed by square of maximum area. Find the number of square designs.  

(A) 10                          (B) 20                    (C) 40                            (D) 80                            (E) None of these

15.      A room, 5m  44cm long and 3m 74cm, broad is to be paved with square tiles. Find the least number of square tiles required to cover the floor.

(A) 170                        (B) 176                  (C) 175                        (D) 180                            (E) None of these

16.      The length of a rectangle is twice its breadth. If its length is decreased by 5 cm and breadth is increased by 5 cm, then the area of the rectangle is increased by 75 sq.cm. Find the length of the rectangle.

(A) 40 cm                  (B) 20 cm           (C) 25 cm                  (D)50cm                             (E) None of these

17.      The length and breadth of a rectangular field are 25 m and 15 m and the two roads each of width 2 m parallel to length and breadth respectively exactly in the centre of field, cut each other and remaining area has grass. The area of grass section is

(A) 295 m²               (B) 299 m²        (C) 300 m²        (D) 375 m²                 (E) None of these

18.      There is 2.5 m broad way around rectangular field whose length and breadth are 40 m and 30 m respectively. The cost of plotting grass on the way at rate of Rs. 3.50 per sq.m is

(A) Rs. 1312.50      (B) 1000               (C) 1012.50                  (D) 1300                      (E) None of these

19.      A rectangular lawn 55 m by 35 has two roads each 4 m wide running in the middle of it, one parallel to length and the other parallel to breadth. The cost of gravelling the roads at 75 paise per sq.m is :

(A) Rs. 254.50             (B) Rs. 258                 (C) Rs. 262.50               (D) Rs. 270                         (E) None of these

20.      A rectangular grassy plot 160 m x 45 m has a gravel path 2.5 m wide all round it on the Inside. Find the cost of gravelling the path at 75 paise per M².

(A) Rs. 5400                 (B) Rs. 7500              (C) Rs. 4650                   (D) Rs. 750                        (E) None of these

21.     The ratio of area of two squares is 9 : 1. Find the ratio of their perimeters.

(A) 5 : 2                         (B) 9 : 1                       (C) 3 : 1                           (D) 81 : 1                            (E) None of these

22.     The side of square is 28 m. The area of circle of  largest radius inscribed in square is

(A) 516 m²                    (B) 196 m²              (C) 616 m²                           (D) 308 m²                     (E) None of these

23.     The perimeters of two squares are 40 cm and 32 cm. Find the perimeter of a third square, whose area is equal to the difference of the areas of the two squares.

(A) 25 cm                      (B) 16 cm                 (C) 20 cm                      (D) 24 cm                              (E) None of these

24.     Area of a square is equal to 1521 sq. cm.  Also length of a rectangle is two-third of the side  of the square and breadth of the rectangle is half of its length. What is the perimeter of the rectangle?

(A) 68 cm                     (B) 78 cm                  (C) 84 cm                      (D) 88 cm                              (E) None of these

25.     The perimeter of a square is twice the perimeter of a rectangle. If the perimeter of the square is 56 cm and the length of the rectangle is 9 cm, then what is the difference between the breadth of the rectangle and the side of the square?

(A) 8 cm                        (B) 9 cm                     (C) 13 cm                      (D) 5 cm                                (E) None of these

26.     What will be the length of the diagonal of that square plot whose area is equal to the area of a rectangle plot of length 45 meters and breadth 40 meters?

(A) 42.5 m                    (B) 60 m                     (C) 75 m                       (D) 80 m                               (E) None of these

27.     A man walked diagonally across a square plot. Approximately, what was the percent saved by not walking along the edges?

(A) 20                             (B) 24                          (C) 30                            (D) 33                       (E) None of these

28.     The diagonals of two squares are in the ratio 5 : 2 Find the ratio of their areas.

(A) 5 : 2                         (B) 25 : 4                    (C) 4 : 25                      (D) 2 : 5                     (E) None of these

29.     If each side of a square is increased by 10%, then find the increase percent in its area.

(A) 20                             (B) 10             (C) 21                              (D) 40                             (E) None of these

30.     The base of a parallelogram is twice its height and its area is 128 cm². Find the base of parallelogram. 

(A) 16 cm                      (B) 8 cm                       (C) 8  cm                     (D) 16 cm                    (E) None of these

31.     The area of a rhombus is 15 cm²and length of a diagonal is 5 cm. The length of another diagonal is

(A) 3 cm                        (B) 5 cm                          (C) 6 cm                          (D) 1.5 cm                         (E) None of these

32.     The area of a rhombus is 64 m². If its one diagonal is twice of another, then the length of larger diagonal is

(A) 8 m                           (B) 10 m                      (C) 16 m                       (D) 24 m                         (E) None of these

33.     A trapezium has a height of 10 cm. Each of its non-parallel sides is 26 cm. Its perimeter is 124 cm. Find its area (In sq.cm.)

(A) 240 cm²                 (B) 390 cm²                    (C) 360 cm²                (D) 345 cm²                         (E) None of these

34.     What will be the area of a circle whose circumference is 132 cm?

(A) 693 cm²                   (B) 264 cm²                 (C) 5227 cm²                  (D) 1876 cm²                    (E) None of these

35.     The perimeters of a circular field and of a square are same. If the area of square field is 121 m², then find the radius of the circle.

(A) 7 m                          (B) 8 m                        (C) 9 m                              (D) 6 m                               (E) None of these

36.     The diameter of a toy wheel is 14 cm. What is the distance travelled by it in 15 revolution?

(A) 880 cm                    (B) 660 cm                  (C) 600 cm                   (D) 560 cm                             (E) None of these

37.     A wire is bent in the form of a circle of 56 cm radius. It is opened and bent to form a square. The side of the square will be.

(A) 16 cm                     (B) 88 cm                      (C) 44 cm                     (D) 56 cm                               (E) None of these

38.     A circle of greatest area is drawn in a rectangular park, having sides 40 m and 28 m respectively. Find the area of park beyond the circle.

(A) 500 m²                     (B) 1120 m²                (C) 504 m²                       (D) 616 m²                    (E) None of these

39.     Find the length of a rope by which a cow must be tethered in order that it may be able to graze an area of 9856 sq. meters.

(A) 56 m                         (B) 35 m                        (C) 28                          (D) 112 m                         (E) None of the

40.     The sum of the circumference of a circle and the perimeter of a square is equal to 272 cm. The diameter of the circle is 56 cm. What is the sum of the area of circle and the area of the square?

(A) 2464 sq. cm           (B) 2644 sq. cm          (C) 3040 sq. cm             (D) 4230 sq. Cm           (E) None of these

41.     The total area of a circle and a rectangle is equal to 1166 sq. cm. The diameter of the circle is 28 cm. What is the sum the circumference of the circle and the perimeter of the rectangle if the length of the rectangle is 25 cm?

(A) 186 cm                    (B) 182 cm                   (C) 184 cm                       (D) 178 cm                  (E) None of these

42.     The difference of the areas of two squares drawn on two line segments of different lengths is 32sq cm. Find the length of the greater line segment if one is longer than the other by 2 cm.

(A) 7cm                         (B) 9cm                       (C) 11cm                      (D) 16cm                    (E) None of these

43.     From four corners of a square sheet of side 4 cm, four pieces, each in the shape of arc of a circle with radius 2 cm, are cut out. The area of the remaining portion is

(A) (8-π)sq.cm             (B) (16-4π)sq.cm         (C) (16-8π)sq.cm       (D) (4-2π)sq. cm        (E) None of these

44.     In measuring the sides of a rectangle, there is an excess of 5% on one side and 2% deficit on the other. Then the error percent in the area is

(A) 3.3%                        (B) 3.0%                        (C) 2.9%                       (D) 2.7%                     (E) None of these

45.     In an isosceles triangle, the measure of each of equal sides is 10 cm and the angle between them is 45⁰. The area of the triangle is

(A) 25 cm²                   (B)  cm²                 (C) 25 cm²              (D) 25 cm²             (E) None of these

46.     The area of the triangle formed by the straight line 3x + 2y = 6 and the co0ordinate axes is

(A) 3 sq units             (B) 6 sq units                 (C) 4 sq units               (D) 8 sq units             (E) None of these

47.     If 2s = a + b + c, then the value of s(s-c) + (s-a) (s-b) is

(A) ab                         (B) abc                             (C) 0                               (D)                     (E) None of these

48.     Two equal maximum sized circular plates are cut off from a circular paper sheet of circumference 352 cm. Then the circumference of each circular plate is

(A) 176cm                  (B) 150cm                      (C) 165cm                      (D) 180cm                  (E) None of these

49.     A horse is tied to a post by a rope. If the horse moves along a circular path always keeping the rope stretched and describes 88 m when it has traced out 72⁰ at the centre the length of the rope is ()

(A) 70m                     (B) 75m                         (C) 80m                             (D) 65m                    (E) None of these 

50.     If the area of a rectangle be (x² + 7x + 10)sq. cm. then one of the possible perimeter of it is

(A) (4x + 14)cm        (B) (2x + 14)cm            (C) (x + 14)cm                   (D) (2x + 7)cm         (E) None of these

51.     The sides of a triangle are in the ratio  :  : . If the perimeter of the triangle is 52cm, the length of the smallest side is

(A) 24cm                    (B) 10cm                      (C) 12cm                             (D) 9cm                    (E) None of these

52.     Through each vertex of a triangle, a line parallel to the opposite side is drawn. The ratio of the perimeter of the new triangle, thus formed with that of the original triangle is

(A) 3 : 2                     (B) 4 : 1                          (C) 2 : 1                              (D) 2 : 3                    (E) None of these

53.     Three circles of diameter 10 cm each are bound together by a rubber band as shown in figure. The length of the rubber band(in cm). If it is stretched as shown is

(A) 30                         (B) 30 + 10π                      (C) 10π                (D) 60 + 20π                   (E) None of these

54.     A gear 12cm in diameter is turning a gear 18 cm in diameter. When the smaller gear has 42 revolutions, how many has the larger one made?

(A) 28                         (B) 20                                (C) 15                    (D) 24                              (E) None of these

55.     The perimeter of a sheet of paper in the shape of a quadrant of a circle is 75cm. Its area would be ()

(A) 100 cm²                (B) 346.5 cm²                 (C) 693 cm²           (D) 512.25 cm²              (E) None of these

56.     ABCD is a parallelogram in which diagonals AC and BD intersect at O. If E, F,G and H are the mid points of AO, DO, CO and BO respectively. Then the ratio of the perimeter of the quadrilateral EFGH to the perimeter of parallelogram ABCD is

(A) 1 : 4                       (B) 2 : 3                            (C) 1 : 2                  (D) 1 : 3                           (E) None of these

57.     ABC is an equilateral triangle of side 2 cm. With A, B, C as centre and radius 1 cm three arcs are drawn. The area of the region within the triangle bounded by the three arcs is

(A) (3 -  ) cm²      (B) ( - ) cm²            (C) ( - ) cm²    (D) (  - ) cm²            (E) None of these

58.     The ratio of length of each equal side and the third side of an isosceles triangle is 3 : 4. If the area of the triangle is 18 sq units, the third side is

(A) 16 units               (B) 5 units              (C) 8 units           (D) 12 units                   (E) None of these

59.     The perimeter of a rhombus is 40 cm and the measure of an angle is 60⁰, then the area of it is          

(A) 100 cm²           (B) 50 cm²               (C) 160cm²            (D) 100 cm²                  (E) None of these

60.     A right angled isosceles triangle is inscribed in a semi-circle of radius 7cm. The area enclosed by the semi-circle of radius 7cm. The area enclosed by the semi-circle but exterior to the triangle is

(A) 14 cm²                  (B) 28 cm²                    (C) 44 cm²                   (D) 68 cm²                   (E) None of these

61.     The area of a regular hexagon of side 2 cm is      

(A) 18 cm²            (B) 12 cm²              (C) 36 cm²              (D) 27 cm²                 (E) None of these

62.     The area of the ring between two concentric circles, whose circumference are 88 cm and 132 cm, is

(A) 780 cm²                  (B) 770 cm²                  (C) 715 cm²                (D) 660 cm²                     (E) None of these

63.     Three circles of radius 3.5 cm each are placed in such a way that touches the other two. The area of the portion enclosed by the circles is

(A) 1.975 cm²            (B) 1.967 cm²               (C) 19.67 cm²             (D) 21.21 cm²                 (E) None of these

64.     Four equal circles each of radius ‘a’ units touch one another. The area enclosed between them(), in square units, is

(A) 3a²                         (B)                            (C)                         (D)                              (E) None of these

65.     A is the centre of circle whose radius is 8 and B is the centre of a circle whose diameter is 8. If these two circles touch externally, then the area of the circle with diameter AB is

(A) 36π                       (B) 64π                        (C) 144π                      (D) 256π                        (E) None of these   

66.     If the difference between areas of the circumcircle and the incircle of an equilateral triangle is 44 cm², then the area of the triangle is ()

(A) 28 cm²                    (B) 7 cm²             (C) 14 cm²              (D) 21 cm²                      (E) None of these

67.     The perimeter of a rectangle is 160m and the difference of two sides is 48m. Find the side of a square whose area is equal to the area of this rectangle.

(A) 32m                       (B) 8m                        (C) 4m                         (D) 16m                            (E) None of these

68.     At each corner of a triangular field of sides 26m, 28m and 30m. A cow is tethered by a rope of length 7m. The area (in m²) ungrazed by the cows is

(A) 336                         (B) 259                      (C) 154                         (D) 77                              (E) None of these

69.     Three circles of radii 4cm, 6cm and 8cm touch each other pair wise externally. The area of the triangle formed by the line-segments joining the centres of the three circles is

         (A) 144sq.cm.     (B) 12sq.cm.  (C) sq.cm.           (D) 24 sq.cm             (E) None of    these