Class 6 Mathematics Case Based Questions Perimeter And Area Summary | Complete Learning Material PDF

Q1: Read the source and answer the question that follows

The figure below shows a square wooden frame of uniform width 1.5 cm enclosing a square picture. 

Q1. What is the area (in cm²) of the frame?
(a) 81
(b) 144
(c) 181
(d) 225

Ans. Option (a) is correct.
Explanation: 

Side of picture = 12 cm
Width of frame = 1.5 cm

Outer side of frame
= 12 + 2 × 1.5
= 12 + 3
= 15 cm

Area of outer square = $152=22515^2\; =\; 225$152=225 cm²
Area of inner square = $122=14412^2\; =\; 144$122=144 cm²

Area of the frame
= 225 − 144
= 81 cm²

Q2. What is the perimeter (in cm) of the picture?
(a) 12
(b) 48
(c) 60
(d) 144

Ans. Option (b) is correct.
Explanation: Perimeter of square = 4a = 4 × 12 = 48 cm

Q2: Read the source and answer the question that follows

Q1. How do you calculate the perimeter of a rectangle?
(a) Length + Width
(b) 2 × (Length + Width)
(c) Length × Width
(d) 4 × Length

Ans: (b) 2 × (Length + Width)
Explanation: The perimeter of a rectangle is calculated by adding the lengths of all four sides, or by using the formula 2 × (Length + Width).

Q2. What is the perimeter of a square with a side length of 7 cm?
(a) 7 cm
(b) 14 cm
(c) 28 cm
(d) 21 cm

Ans: (c) 28 cm
Explanation: The perimeter of a square is 4 times the length of one side. So, 4 × 7 = 28 cm.

Q3. If a rectangular garden has a length of 12 meters and a width of 4 meters, what is its perimeter?
Ans: The perimeter is 2 × (12 + 4) = 32 meters.

Q3: Read the source and answer the question that follows.

Sanjay and Meera were tasked with calculating the area of different shapes. Sanjay designed a rectangular path with a length of 50 meters and a width of 20 meters. Meera created a square path with each side measuring 25 meters. Sanjay calculated the perimeter of his rectangular path as 2 × (50 + 20) = 140 meters and the area as 50 × 20 = 1000 square meters. Meera calculated the perimeter of her square path as 4 × 25 = 100 meters and the area as 25 × 25 = 625 square meters. Sanjay was amazed to find that even though Meera's path had a smaller perimeter, it covered less area.

Q1. If a rectangle has a length of 15 meters and a width of 10 meters, what is its perimeter?
(a) 30 meters
(b) 50 meters
(c) 25 meters
(d) 40 meters
Ans: (b) 50 meters
Explanation: The perimeter of a rectangle is 2 × (Length + Width), 
so 2 × (15 + 10) = 50 meters.

Q2. What is the area of a square with a side length of 6 meters?
(a) 12 m²
(b) 36 m²
(c) 24 m²
(d) 18 m²
Ans: (b) 36 m²
Explanation: The area of a square is side × side, so 6 meters × 6 meters = 36 square meters.

Q3. How would you calculate the total area if you want to plant flower beds of size 4 meters by 4 meters in a rectangular garden of size 12 meters by 8 meters?

Ans: The area of the garden is 12 meters × 8 meters = 96 m²
If each flower bed is 4 meters by 4 meters, the area of one flower bed is 4 × 4 = 16 m². 

Number of beds that fit:
Along length: $12\; \backslash div\; 4\; =\; 3$12 ÷ 4 = 3
Along width: $8\; \backslash div\; 4\; =\; 2$8 ÷ 4 = 2

Total beds = $3\; \backslash times\; 2\; =\; 6$3 × 2 = 6

Total planted area = 6×16=96 m²