Practice Questions with Solutions: Perimeter and Area

Q1: Length of a rectangular park is 3 times its breadth. If the length of the park is 90 metres, then find the area of the park.
Ans: Length of rectangular park = 90 m.
So, breadth = 90 m ÷ 3 = 30 m.
Area of the rectangle = length × breadth
= 90 m × 30 m = 2700 m².

Q2: Find the area of a rectangular piece of cardboard measuring 1 m long and 25 cm broad.
Ans: Length is in metres, but the breadth is in cm. So, we change the length to cm.
1 m = 100 cm, so length = 100 cm.
Area = length × breadth
= 100 cm × 25 cm = 2500 cm².

Q3: Find the area of a square with a side of 7 cm.
Ans: Area of a square = side × side
= 7 cm × 7 cm = 49 cm².

Q4: Find the Perimeter (P) and the Area (A) of the Given Figures. Assume Each Side of the Unit Square is 2 Cm

Ans: Each small square has a side = 2 cm.
Perimeter is the length of the continuous outer boundary of the figure.

Perimeter of the given figure is found by adding the lengths of all outer edges.
As shown in the figure, the outer edges add up to (2 + 2 + 2 + 2) + (2 + 2 + 2) + 2 + 2 + (2 + 2) + 2 + 2 + 2 = 28 cm.
∴ Perimeter of the given figure = 28 cm.
Now for area;
Area of one small square = side × side = 2 cm × 2 cm = 4 cm².

There are 8 such small squares in the figure.
Area of the figure = area of one square × number of squares = 4 cm² × 8 = 32 cm².

Q5: Find the Perimeter of and the area of the figure below:
Side = 30Ans: A square has all four sides equal. Here, each side = 30 cm.
Perimeter of square = 30 + 30 + 30 + 30 = 120 cm.
Area of square = side × side = 30 cm × 30 cm = 900 cm².

Q6: Find the Perimeter and Area of the rectangle below 
Length = 4m 20cm and Breadth = 2m and 50cm
Ans: First convert length and breadth to the same unit (use cm).
1 m = 100 cm.
Length = 4 m 20 cm = (4 × 100) cm + 20 cm = 400 cm + 20 cm = 420 cm.
Breadth = 2 m 50 cm = (2 × 100) cm + 50 cm = 200 cm + 50 cm = 250 cm.
Perimeter of rectangle = 2 × (length + breadth)
= 2 × (420 cm + 250 cm) = 2 × 670 cm = 1340 cm.
Area of rectangle = length × breadth = 420 cm × 250 cm = 105000 cm².

Q7: Neha and Rekha Draw a Circle of the Same Size in Their Books
If the length and breadth of Neha՚s Book is 60 cm and 40 cm, and the length and Breadth of Rekha՚s Book is 70 Cm and 30 Cm, Find Whose Book Have More Circle?
Ans: Area of Neha's book = 60 cm × 40 cm = 2400 cm²(length × breadth)
Area of Rekha's book = 70 cm × 30 cm = 2100 cm²(length × breadth)
Since 2400 cm² > 2100 cm², Neha's book has the larger area. If both draw circles of the same size, Neha's book can fit more such circles than Rekha's book.

Q8: An Open Cinema Ground is 240 Meter Long and 190 meters in Breadth
Find the area of land acquired by Open Cinema.
Ans: Length of an open cinema ground is 240 meters and breadth is 190 meters.
Means it's a rectangular shape.
Now for the perimeter of the rectangle;
Area of open cinema ground = length × breadth
∴ Area of open cinema ground = 240 × 190
∴ Area of open cinema ground = 45600 m²
Therefore, the area of the Open cinema ground is 45600 m².

Q9: Answer the Following Questions. (Every Room is a Square or a Rectangle)

(i) Look at the house design and find the area of the bathroom.
Ans: The bathroom is a rectangle with length 11 and breadth 3 (units as given).
Area = length × breadth = 11 × 3 = 33 (units)².

(ii)  Look at the house design and find the area of the kitchen.
Ans: The kitchen is a rectangle with length 24 and breadth 4 (units as given).
Area = length × breadth = 24 × 4 = 96 (units)².

Q10: Find the length of the rectangular school playground of 4800 square meters and 60 m in breadth.
Ans: Area = length × breadth.
4800 m² = length × 60 m.
Length = 4800 m² ÷ 60 m = 80 m.
Therefore, the length of the playground is 80 m.