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Quiz: Perimeter and Area

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Number of Questions: 31

Question: 1 -

The base of a right-angled triangle is 10 and hypotenuse is 20. What is its area?

Options:

  1. 58 meters

  2. 52 meters

  3. 68 meters

  4. 60 meters

    5. Answer:

    60 meters
    Solution:

    The area of a right angled triangle = ½ * base * height

    Base = 10, Hypotenuse = 20
    Height2 = Hypotenuse2 - Base2
                       = 202 - 162
                       = 400 - 256
          Height2 = 144
          Height = 12

    Area = ½ * base * height

                   = ½ * 10 * 12
                   = 60 meters

Question: 2 -

The perimeter of the rectangular field is 480 meters and the ratio between the length and breadth is 5:3. Find the area of the field.

Options:

  1. 54000 m2

  2. 7200 m2

  3. 15000 m2

  4. 13500 m2

    5. Answer:

    13500 m2
    Solution:

    Let the length of the rectangle be 5x, and breadth be 3x,
    Perimeter of a rectangle = 2(l +b) = 480
                                             2(5x + 3x) = 480
                                             2 x 8x = 480
                                             16x = 480
                                             x = 480/16 = 30

    ∴ Length = 5 x 30 = 150 m
                      Breadth = 3 x 30 = 90 m

    And, Area of rectangle = L x B
                                         = 150 x 90 = 13500 m2

Question: 3 -

The ratio of length and breadth of a rectangular park is 4:2. If a cat running along the boundary of the park at the speed of 18 km/hr completes one round in 10 minutes, find the area of the park in square meters.

Options:

  1. 68000 sq. m

  2. 50000 sq. m

  3. 45000 sq. m

  4. 55000 sq. m

    5. Answer:

    50000 sq. m
    Solution:

    One round of the park is equal to the perimeter of the park.

    So, by completing one round, the cat covers a distance equal to the perimeter of the park.

    Now, Distance or perimeter = speed * time
                                                = 18 * (10/60)
                                                = 3 km or 3000 meters

    Let Length = 4x and breadth = 2x

    So, Perimeter: 2 (4x + 2x) = 3000
    8x + 4x = 3000
    12x = 3000
    x= 3000/12= 250 meters

    So, Length = 4 * 250 = 1000 meters

    And, Breadth = 2 * 250 = 500 meters

     

    Area = Length * Breadth
          = 1000 * 500
          = 50000 sq. m.

Question: 4 -

The sides of a triangle are in the ratio 10: 24:26 and its perimeter is 300 m. What is its area?

Options:

  1. 3000 m2

  2. 4000 m2

  3. 2500 m2

  4. 3500 m2

    5. Answer:

    2500 m2
    Solution:

    Let the sides are 10x, 24x, and 26x.
    The perimeter is 300 m.
    So, 10x + 24x + 26x = 300
    60x = 300
    x= 5

    So, the sides are 10 *5 = 50 meters
    24 * 5 = 100 meters
    26 * 5 = 130 meters
    102 + 242 = 262 so, it is a right triangle.
           100 + 576 = 676

    The area of a right triangle is = 1/2 * base * height
                  = 1/2 * 50 * 100
                  = 2500 m2

Question: 5 -

What is the area of a triangle with base 5 meters and height 10 meters?

Options:

  1. 40 square meters

  2. 20 square meters

  3. 35 square meters

  4. 25 square meters

    5. Answer:

    25 square meters
    Solution:

    Area of a triangle = ½ * base * height
    So, the area = ½* 5 * 10
                       =25 square meters