Area and Perimeter Questions

One of the most interesting yet trickiest topics of mathematics is area and perimeter. The beginner level questions may sound interesting and simple, but as you move further, you will come across a bunch of perplexing questions. Problems based on area and perimeter are not only included in the school curriculum but also form an essential part of the syllabus of Maths for competitive exams. Hence, it becomes essential to develop a strong understanding of the concepts related to the topic. In this blog, we have collated a list of area and perimeter questions for you to solve. So, pull up your socks and let’s get started! 

Area and Perimeter Formula Chart 

Area formulas for different geometrical figures are: 

Figures	Area Formula	Variables
Area of Rectangle	Area = l x w	l = Length w = Width
Area of Square	Area = a x a	a = sides of the square
Area of Triangle	Area = ½ b x h	b = Base h = Height
Area of Circle	Area = π r²	r = Radius of the Circle
Area of a Trapezoid	Area = ½ ( a + b) h	a = base 1b = base 2h = vertical height
Area of Ellipse	Area = πab	a = radius of the major axis b = radius of the minor axis

Perimeter formulas for different geometrical figures: 

Figures	Perimeter Formula	Metrics
Parallelogram	2(Base + Height)	l = Lengthw = Width
Triangle	a + b + c	a,b and c being the side lengths
Rectangle	2(Length + Width)
Square	4a	a = Length of side
Trapezoid	a + b + c + d	a,b, c, and d is the side lengths
Kite	2ab + 2b	a = length of the first pair of equal sides b = length of the second pair of equal sides
Rhombus	4 x a	a = Length of a side
Hexagon	6 x a	a = Length of a side

Area and Perimeter Questions: SET 1

1. A playground which is 60 metres long and 40 metre broad has a special path for jogging which is 1 metre wide. You need to determine the total area of the playground. 
2. Rohit has a rectangular pencil box with dimensions 8cm, 6cm and 2cm. Find the maximum length of a pencil that can be kept inside the pencil box. 
3. A circle is formed using a ribbon which has a radius of 28 cm. If a square has to be formed using the same ribbon, determine the length of the side of the square formed using the ribbon. 
4. Find out the area of a square, the diagonal’s length of which is 40 cm. 
5. 7 cm, 9cm and 11 cm are the dimensions of a triangle. Calculate the total area of the same.  

Area and Perimeter Questions: SET 2

1. A park has two circular running tracks. If 20cm is the difference between the two circumferences of both the circular tracks, determine what will be the width of the track?
2. Island in the form of a parallelogram has to be levelled. The cost of levelling the land would be 20 rupees per 10 square metre. The length of the base and the perpendicular distance from the other side of the parallelogram are 25 cm and 32 cm respectively. Find out the total cost of levelling the field as per the given price. 
3. There is a piece of land which is rectangular in shape. Its perimeter is 250 cm and the breadth is 80 cm. What will be the length and area of the rectangle? 
4. A plot which is rectangular in shape has to be tilled. If the length of the plot is 200m and the breadth is 125mand the cost of tiling per 100 square feet is Rs 50, what will be the total cost of tilling the land? 
5. Determine the total number of rectangles that can be drawn if the total perimeter is 40cm. Along with this, find the dimensions of the rectangle which has the smallest area.

Questions SET 3

Now that you are through with the aforementioned area and perimeter questions, let us solve some tricky ones!

1. There is a rectangle whose total area is 400 m². If the length of the rectangle is 100 m, then find the breadth and perimeter of the rectangle. 
2. The wedding hall needs renovation and its floor has to be covered with a carpet. The cost of carpeting the floor is 100 rupees per square meter. The restaurant is 14 meters wide and 16 meters long. Find the total cost it will take to complete this process. 
3. There is a rectangle whose breadth is thrice its length. If the length is 128 cm, determine the cost of fencing the rectangle at a cost of 20 rupees per square meter. 
4. A lawn with dimensions 400 cm length and 138 cm breadth needs to be covered with tiles. How many tiles with dimensions 5 cm X 12 cm will be needed to cover the land having the aforementioned dimensions. 
5. A parallelogram with area 256 cm square has a base of 25cm. Determine the length of the two sides of this parallelogram. 

Hence, to score well, it is very important to practice area and perimeter questions on a regular basis. We, at Leverage Edu, provide expert guidance related to stream selection, how to choose a career path after class 12, university admission, etc. To avail the benefits of our services, book an e-meeting session with our experts. Hurry up!