NCERT Solutions for Mensuration Class 8 Maths Chapter 11 CBSE Part 1

Question 1
A square and a rectangular field with measurements as given in the figure have the same perimeter. Which field has a larger area?

Answer: Perimeter of Square   is given by
= 4 x side = 4 x 60 = 240 m
Area of Square = Side² = 60² = 3600 m²
Now Perimeter of Rectangle is given by
= 2(length + breadth)
Or, = 2(80 + breadth)
Now both the square and rectangle has the same perimeter
So
240=2(80 + breadth)
80 + breadth = 120
Breadth = 120-80 = 40 m
Area of rectangle = length x breadth = 80 x 40 = 3200 m²
Now it is clear that the area of the square field is greater than the area of the rectangular field.
Question 2
 Mrs. Kaushik has a square plot with the measurement as shown in the figure. She wants to construct a house in the middle of the plot. A garden is developed around the house. Find the total cost of developing a garden around the house at the rate of Rs 55 per m².

Answer: Area of the square plot = Side² = 25² = 625 m²
Area of the house construction part = length x breadth
= 20 x 15 = 300 m²
So, area of the garden = Area of square plot – area of house in construction=625-300=325 m²
Cost of developing the garden = Area  of Garden x Rate
= 300 x 55 = 16500 rupees
Question 3
 The shape of a garden is rectangular in the middle and semicircular at the ends as shown in the diagram. Find the area and the perimeter of this garden [Length of rectangle is 20 – (3.5 + 3.5) m].


Answer: Area of the rectangular part = length x breadth
= 20 x 7 = 140 sq m
Area of Semicircular portions: = ? x r²
Here ?=22/7   and radius =7/2=3.5 m
So area of two Semicircular portions: =Area of circle= ? x r²
= (22/7) × 3.5 ×3.5= 37.5
So Total area of the garden=
Area of rectangular portion + Area of circle
=140+37.5=177.5 m²
Now the perimeter of shape= Perimeter of semicircular portion + Length+ Perimeter of semicircular portion + length
=Perimeter of Circle + 2 Length
= 2 ? r + 40
=22+40=62 m


Question 4
 A flooring tile has the shape of a parallelogram whose base is 24 cm and the corresponding height is 10 cm. How many such tiles are required to cover a floor of area 1080 m²? (If required you can split the tiles in whatever way you want to fill up the corners).
Answer: Area of the Parallelogram = base x height
= 24 x 10 = 240 cm²
So required Number of tiles = Area of the Floor/Area of the Tiles
= 1080 X100 X100/240  =45000
(area of floor is converted into square cm)
Question 5
 An ant is moving around a few food pieces of different shapes scattered on the floor. For which food-piece would the ant have to take a longer round? Remember, circumference of a circle can be obtained by using the expression c = 2πr, where r is the radius of the circle.

Answer

1.  In the first case, Perimeter of the shape = Perimeter of Semicircular part + Diameter of the part
   = ?r + 2r
   =(22/7) × (1.4)  + 2.8
   =7.2 cm
   
2. In the second case, Perimeter of the shape = Perimeter of Semicircular part + 2Length + Breath
   = ?r +2 L + B
   =4.4 + 3 +2.8
   =10.2 cm
   
3. In the third case, Perimeter of the shape = Perimeter of Semicircular part + 2(slant height)
   =4.4 + 4=8.4 cm
   

So, the food shape in (a) requires the ant to cover the least distance.

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Class 8 Maths Class 8 Science