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Quiz: Perimeter and Area

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Number of Questions: 31

Question: 11 -

If the area of the trapezium, whose parallel sides are 6 cm and 10 cm is 32 sq. cm, what will be the distance between the parallel sides?

Options:

  1. 8

  2. 5

  3. 4

  4. 2

    5. Answer:

    4
    Solution:

    Parallel sides of a trapezium = 6 cm, and 10 cm
    Area of trapezium = Area Aptitude( sum of the parallel sides ) × distance between the parallel sides
                                      32= Area Aptitude( 6+10 ) × distance

                                      32=8 × distance

                                      Distance = 32/8 = 4 cm

    So, the distance between the parallel lines of trapezium = 4 cm.

Question: 12 -

What is the area of a square field whose diagonal is 40 meters?

Options:

  1. 900 sq. m

  2. 750 sq. m

  3. 800 sq. m

  4. 950 sq. m

    5. Answer:

    800 sq. m
    Solution:

    Area of a square = 1/2 (diagonal) 2

                    = 1/2 (40)2

                    = 1/2 * 1600

                    = 800 sq. m.

Question: 13 -

What is the area of a square field whose side is 20 meters?

Options:

  1. 350 sq. m

  2. 400 sq. m

  3. 450 sq. m

  4. 300 sq. m

    5. Answer:

    400 sq. m
    Solution:

    The area of a square = (side) 2
                                      = (20)2
                                      = 400 sq. m.

Question: 14 -

A rectangular grass field has a length of 85 meters and breadth of 65 meters. It is surrounded by a 5-meter wide path. Find the area of the Path and the cost of constructing it at Rs. 5 per square meter?

Options:

  1. 6000

  2. 7000

  3. 8000

  4. 4000

    5. Answer:

    8000
    Solution:

    Area of the entire grass field including the path = Length (85 + 5 +5) * Breadth (65 + 5+5)
                                                                                = 95 * 75 = 7125 sq. m.

    Area of the grass field excluding the path = 85 * 65 = 5525 sq. m.

    So, area of the path = 7125 - 5525 = 1600 sq. m.

    The cost of constructing is Rs. 5 per square meter.

    So, the cost of constructing the entire path = 1600 * 5 = Rs. 8000

Question: 15 -

The length of a rectangle is thrice its breath, and its perimeter is 106 meters. What is its area?

Options:

  1. 509 sq. m

  2. 510 sq. m

  3. 508 sq. m

  4. 507 sq. m

    5. Answer:

    507 sq. m
    Solution:

    Let the breath = x

    So, the Length = 3x

    Perimeter of a rectangle = 2 (Length + Breadth)
                                          So, 2 (3x + x) = 106
                                          6x + 2x = 106
                                          8x = 106
                                          x = 104/8 = 13

    Now, Breadth = 13, so, length = 13 * 3 = 39

    So, its area = Length * Breadth
                         = 39 * 13 = 507 sq. m.