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 `=4xx\text(side)=4xx60=240` metres
Area of Square = Side² `= 60^2 = 3600` square metre
Perimeter of Rectangle = 2(length + breadth)
Or, `240 = 2(80 + text(breadth))`
Or, `80 + text(breadth) = 120`
Or, breadth `= 120-80 = 40` metres
Area of rectangle = length x breadth `= 80 xx 40 = 3200` square metres
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 `= 25^2 = 625` square metre
Area of the house construction part = length x breadth
`= 20 xx 15 = 300` sq m
So, area of the garden `= 625-300=325` square metre
Cost of developing the garden = Area x Rate
`= 300 xx 55 = 16500` rupees
Question 3: The shape of a garden is rectangular in the middle and semi circular 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) metres].
Answer: Area of the rectangular part = length × breadth
`= 20 xx 7 = 140` sq m
Area of Semicircular portions: `=πr^2`
`=(22)/7×3.5^2=11×3.5=38.5` sq m
Perimeter of the shape = Perimeter of circle + 20 + 20
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 xx 10 = 240` sq cm
Required number of tiles `=text(Area of floor)/text(Area of tile)`
(area of floor is converted into square cms)
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: (a) Perimeter `=(πd)/(2)+d`
(b) Perimeter `=(πd)/(2)+2xx\text(breadth)+text(length)`
(Perimeter of semicircular part is same as in (a))
(c) Perimeter `=(πd)/(2)+2xx\text(slant height)`
So, the food shape in (a) requires the ant to cover the least distance.