Maths - Perimeter and Area

• Perimeter of a closed plane figure is the length of its boundary.
• Area of a closed plane figure is the measure of the region (surface) enclosed by its boundary.
• Area of a triangle: Area of a triangle = (1/2) × base × height
  Also, Area of a triangle = [s (s -a)(s -b)(s-c)] where a, b, c are the lengths of the sides and s = (a +b +c)/2
  Area of an equilateral triangle = 3a²/4, where a is the side.
• Rectangle: If l = length and b = breadth of a rectangle, then perimeter = 2 (l +b)
  length of diagonal = l²+b², area = l×b.
• Square: If a is the length of side of a square, then perimeter = 4a
  length of diagonal = 2 a, area = a²
• Circle: If r is the radius of a circle, then length of a diameter = 2r
  circumference = 2r, area = r²
  Take = 22/7 (unless given otherwise)
• Circular ring (track): If R and r are the radii of two concentric circles then
  area of the circular ring (track) = (R²-r²).

                                         Exercise

1. The length of a room is 5.5 m and width is 3.75 m . Find the cost of paving the floor by slabs at the rate of Rs 800 per sq m(in Rs).

          a. 15000 b. 15550 c. 15600 d. 16500 e. None

2. The length of a ractangle plot is 60% more than its breadth. If the diffrence between the length and breadth of that reactangle is 24 cm, what is the area of that ractangle?

          a. 2400 sq cm b. 2480 sq cm c. 2560 sqcm d. Data inadequate e. None

3. The length of a ractangle plot is 20 m more than its breadth. If the cost of fencing the plot @ Rs 26.50 per meter is Rs. 5300, what is the length of the plot in meters.

         a. 40 b. 50 c. 120 d. Data inadequate e. None

4. The ratio between the length and the perimeter of a ractangle is 1 : 3. What is ratio between the length & breadth of the plot?

          a. 1:2 b. 2:1 c. 3:2 d. Data inadequate e. None

5. A ractangular field is to be fenced on three sides leaving a side of 20 ft uncovered. If the area of the field is 680 sq feet, how many feet of fencing will be required?

          a. 34 b. 40 c. 68 d. 88 e. None

6. The ratio between the perimeter and breadth of a ractangle is 5:1. If the area of the ractangle is 216 sq cm. The length is:

          a. 16 cm b. 18 cm c. 24 cm d. Data inadequate e. None

7. A towel when bleached, was found to have lost 20% of its length and 10% of width. The % decrease in area is:

          a. 10 b.15 c. 20 d. 28 e. None

8. What will be the length of the diagonal of that square plot whose area is equal to the area of a ractangular plot of length 45 mt and breadth 40 mt?

          a. 42.5 b. 60 c. 75 d. Data inadequate e. None

9. If the side of a square is increased by 5 cm, the area increases by 165 sq cm. The side of the square is:

        a. 12 b. 13 c. 14 d. 15 e. None

10. The base of a tringle is 15 cm height is 12 cm. The height of the another tringle of the double the area having base 20cm is:

        a. 8 b. 9 c. 12.5 d. 18 e. None

11. The area of a right angle tringle is 40 times its base. What is its height?

        a. 45 b. 60 c. 80 d. Data inadequate e. None

12. The sides of a tringle are in ratio ½:1/3:1/4. if the perimeter is 52cm. Than the length of the smallest side is:

        a. 9 b. 10 c. 11 d. 12 e. None

13. The area of a circle of radius 5 is numerically what % of its circumference?

        a. 200 b. 225 c. 240 d. 250 e. None

14. A circle and a ractangle have the same perimeter. The sides of the ractangle are 18 & 26 cm. The area of circle is:

        a. 88 b. 154 c. 1250 d. Cant find e. None

15. A circular wire of radius of 42 cmis bent in the form of a ractangle whose sides are in ratio 6:5. Smaller side of ractangle is:

        a. 25 b. 30 c. 36 d. 60 e. None

  Ans: 1d, 2c, 3e, 4b, 5d, 6b, 7d, 8b, 9c, 10d, 11c, 12d, 13d, 14e, 15d