Page 185 - Ganit Kaushal

17. In the adjoining figure, find the area of the path shaded, which is 2 metres wide 100 m
all around.
18. The perimeter of a square is equal to that of a rectangle of length 17 metres 60 m
and breadth 11 metres. Find the area of the square.
19. Find the area of the shaded region in the following figures by using conventions C1 – C4 and by
splitting into triangles and rectangles. Ensure you get the same answer by both methods.

(a) (b) (c) (d) (e) (f)
20. A square and a rectangle have equal perimeters. The side of the square is 60 metres, and the length of
the rectangle is 90 metres. Which shape has a greater area and by how much?

21. Ram wants to cover the floor of a room 6 metres wide and 4 metres long with square tiles. If each square
tile has a side of half a metre, then find the number of tiles required to cover the floor of the room.
22. Split the adjoining shapes into rectangles and 2 7 5
find their areas (the measures are given in 7 7 7 7 1 2 2 1
centimetres). 12 10 7 7

8 7 7 4
2 7 7
10 7
(a) (b) (c)
23. In the adjoining figure, A, B and C are squares. If the area of square A is 25 sq. cm
and the perimeter of square B is 12 cm, then find the perimeter and area of B
square C. A C
24. Find the least and the greatest possible perimeters of a rectangle with area 36 sq cm.
Assertion Reason Type Questions

A statement of assertion (A) is followed by a statement of reason (R). Choose the correct option out of the
choices given below for each question:
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.
1. Assertion (A): The area and perimeter of a given shape always have the same units.

Reason (R): The area of a closed plane figure measures the region enclosed by its boundary.
2. Assertion (A): Sheila has two wires, each 27 metres long. Sheila bent one into a circle and the other
into an equilateral triangle. Both shapes have the same perimeter.
Reason (R): The perimeter of a closed shape is the length of its boundary.
3. Assertion (A): Rama has two wires, each of length 40 metres. She bends one wire into a square, and the
other into a rectangle, having length 15 metres and width 5 metres. Both shapes have the same perimeter.
Reason (R): Both shapes have the same area.

Perimeter and Area 183