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Quiz: Perimeter and Area

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Number of Questions: 31

Question: 21 -

A blanket, when bleached, decreases in length by 20% and in breadth by 15%. What is the percentage decrease in its area?

Options:

  1. 45

  2. 42

  3. 32

  4. 35

    5. Answer:

    32
    Solution:

    Let original length = X

    Original breadth = Y

    So, original area = XY
    So, decrease in area = X*Y - Area Aptitude

    Area Aptitude

Question: 22 -

The difference between the length and breadth of a rectangle is 25 meters. If the perimeter of this rectangle is 210 meters, what is its area?

Options:

  1. 3000 

  2. 3600 

  3. 2000 

  4. 2600 

    5. Answer:

    2600 
    Solution:

    The perimeter: 2 (L + B) = 210 or L+ B = 105 ...... (i)

    As per the question: (L - B) = 25 ....... (ii)

    Solving the above two equations:

    L + B = 105

    B = 105 - L

    Put the value of B in (ii).

    L - (105 - L) = 25

    L - 105 + L = 25

    2L = 25 + 105

    2L = 130

    L = 65

    So, - B = 105 - 65 = 40

    Now, area of a rectangle: L *B= 65 * 40 = 2600 m2

Question: 23 -

The area of a trapezium is 1500 sq. m. If the parallel sides are in the ratio of 12: 18 and the distance between the parallel sides is 32 meters, what is the length of the smaller parallel side?

Options:

  1. 4.5

  2. 6.5

  3. 3.3

  4. 5.3

    5. Answer:

    3.3
    Solution:

    Trapezium is a quadrilateral with one pair of parallel sides.

    Let the length of the smaller side = 12x

    Length of the bigger parallel side = 18x

    Distance between parallel sides = 32 meters

    Area of a trapezium = 1/2 * (sum of parallel sides) * distance between them.

    So, as per the question: 1500 = 1/2 (12x +18x) * 30

                                      1500 = 1/2 * 30x * 30

    1500 = 30x * 15

    30x = 1500 /15

    30x = 100

    x= 100 /30 = 3.3 meters

Question: 24 -

The area of a parallelogram is 162 square meters. If its altitude is twice the corresponding base, find the length of the base?

Options:

  1. 9

  2. 8

  3. 7

  4. 10

    5. Answer:

    9
    Solution:

    Area of a parallelogram = (Base * Height)

    Let the length of the base is = X

    Then, the altitude or height is = 2X

    So, Area: X * 2X = 162 sq. m.

    2X2 = 162

    X2 = 81

    X = 9 meters (length of the base).

Question: 25 -

The side of a rhombus is 25 m, and one of its diagonal is 30 meters. What is its area?

Options:

  1. 500 sq. m

  2. 400 sq. m

  3. 600 sq. m

  4. 450 sq. m

    5. Answer:

    600 sq. m
    Solution:

    Diagonal of a rhombus bisect and divide each other equally.

    So, half of the given diagonal = 15 m.

    Let the half of the other diagonal = X

    So, as per the Pythagoras theorem: 152 + X2 = 252

                                      225 + X2 = 625

                                      X2 = 625 - 225

                                      X2 = 400

                                      X = 20

    So, the length of the other diagonal is double of X: 20 + 20 = 40 m.

    Now, Area of a rhombus = 1/2 * (product of diagonals)

                                 = 1/2 * 30 * 40
                                 = 600 sq. m.