NCERT Solutions Class 7 Mathematics Chapter 11: Perimeter and Area
Class 7 introduces students to several new Mathematics topics and concepts, which will be further built upon in higher grades. This makes it very important that Class 7 students focus on building a strong foundation in this subject at this stage.
Students can use the NCERT Solutions for Class 7 Mathematics Chapter 11 by Extramarks for their preparations. They can get detailed and accurate solutions to questions given in the NCERT textbook, which will help them understand how to solve the different kinds of problems in a step-by-step manner. If they ever get stuck on a question, they can always refer to the solutions prepared by subject matter experts.
NCERT Solutions Class 7 Mathematics Chapter 11 –
Access NCERT Solutions for Class 7 Mathematics Chapter 11 – Perimeter and Area
NCERT Solutions for Class 7 Mathematics Chapter 11 –
NCERT Class 7 Mathematics Chapter 11 teaches students how to calculate the perimeters and areas of different types of basic shapes, including squares, circles, triangles and parallelograms. Students are introduced to a lot of different formulas that they must remember and retain to perform well in the exam. They are also taught about how to handle the conversion of measurement units.
Some of the core concepts and formulas included in the chapter are as follows:
- Perimeter is the total length of the boundary of a closed rectilinear figure.
- The surface circled by a two-dimensional figure is its area.
- Area of a Parallelogram = Base × Altitude
- Area of a Triangle = ½ × Base × Altitude corresponding to the base
- Circumference of a circle = 2πr.
- Area of a Circle = πr²
- 1 cm² = 100 mm²
- 1m² = 10000 cm²
- 1 hectare = 10000 m²
- The perimeter of a regular polygon = Length of a side × Number of the sides
Triangle: A triangle is a plane figure surrounded by three lines segments.
Rectilinear Figure: A plane figure encompassed by line segments is called a rectilinear figure. None of the two sides of it intersects at a point other than the vertex.
Quadrilateral: It is a plane figure surrounded by four long segments.
Parallelogram: Parallelogram is a plane figure encircled by four long segments. The opposite sides of a parallelogram are equal and parallel in length.
Area of a Triangle: The area of a triangle is ½ × Base × Height (Altitude corresponding to the base).
Example: base = 6 cm, height = 12cm. What is the area of a triangle?
As the formula goes; ½ × Base × Height
= (½ × 6 × 12) cm² = 36 cm²
Area of a Parallelogram: Base × Altitude (height)
Example: base = 10 cm and height = 5 cm
The formula of parallelogram: base × height
= (10 × 5) cm²
= 50 cm²
Circumference of a Circle: Perimeter of a circle is similar to the circumference of a circle. The students would draw four circles of different radii and find their circumference with the ratio of the circumferences to the diameter. The ratio will be more than three times its diameter.
Area of a Circle: The area a circle occupies on a flat plane which has its length and breadth, is known as the area of a surface. The formula to find the area is πr².
Conversion of Units
Units of Length
Units of Area
|1 cm = 10 mm||1 cm² = (10 x 10) mm² = 100 mm²|
|1 dm = 10 cm||1 dm² = (10 x 10) cm² = 100 cm²|
|1 m = 10 dm||1 m² = (10 x 10) dm² = 100 dm²|
|1 dam = 10 m||1 dam² = (10 x 10) m² = 100 m²|
|1 hm = 10 dam||1 hm² = ( 10 x 10 ) dam² = 100 dam²|
|1 km = 10 hm||1 km² = ( 10 x 10) hm² = 100 hm²|
1m = 100 cm ∴ 1 m² = 10000 cm²
1 km = 1000 m ∴ 1 km² = 10, 00, 000 m²
1 hectare (ha) = 100 m x 100m = 10000 m²
NCERT Solutions for Class 7 Mathematics
Mathematics is that one subject that many students struggle with. This is because getting good at Mathematics requires one to practise solving many problems and most students don’t do that. With NCERT Solutions of Class 7 Mathematics, Extramarks tries to provide students with a very valuable resource that they can use to get better at the subject and eventually score well in their final exams. Students can use these solutions if they ever get stuck on a problem or to learn the approach to how to solve the different kinds of problems encountered in any NCERT Mathematics Class 7 Chapter 11.
The NCERT Solutions by Extramarks are prepared by subject matter experts who give special attention to providing detailed and accurate solutions in a step-by-step manner so that students can easily grasp the problem-solving approach. Students can use these resources for their preparations, last-minute revisions, and for help with their assignments.
NCERT Solutions for Class 7
Apart from Mathematics, Extramarks provides comprehensive solutions to textbook questions for all of the other subjects covered in Class 7. All the solutions are prepared by their respective subject experts and extra care is given to providing accurate solutions which students can rely on. Students can download all these solutions from the Extramarks website.
Q.1 Find the area of a square park whose perimeter is 320 m.
Q.2 Find the breadth of a rectangular plot of land, if its area is 440 m2 and the length is 22 m. Also find its perimeter.
Q.3 The perimeter of a rectangular sheet is 100 cm. If the length is 35 cm, find its breadth. Also find the area.
Q.7 Find the area of each of the following parallelogram :
Q.8 Find the area of each of the following triangles :
Q.9 Find the missing values :
|S. NO.||Base||Height||Area of the Parallelogram|
|a.||20 cm||246 cm2|
|b.||15 cm||154.5 cm2|
|c.||8.4 cm||78.72 cm2|
|d.||15.6 cm||16.38 cm2|
Q.10 Find the missing values :
|Base||Height||Area of Triangle|
|15 cm||……………..||84 cm2|
|……………..||31.4 mm||1256 mm2|
|22 cm||……………..||170.5 cm2|
Q.17 If the circumference of a circular sheet is 154 m, find its radius. Also find the area of the sheet. (Take π =
Q.18 From a circular sheet of radius 4 cm, a circle of radius 3 cm is removed. Find the area of the remaining sheet. (Take π = 3.14)
Q.19 Find the perimeter of the adjoining figure, which is a semicircle including its diameter.
The circumference of a circle is 31.4 cm. Find the radius and the area of the circle ? (Take π = 3.14)
Q.24 A circular flower bed is surrounded by a path 4 m wide. The diameter of the flower bed is 66 m. What is the area of this path? (π = 3.14)
Q.26 Find the circumference of the inner and the outer circles, shown in the adjoining figure? (Take π = 3.14)
Q.27 How many times a wheel of radius 28 cm must rotate to go 352 m? (take π =
Q.28 The minute hand of a circular clock is 15 cm long. How far does the tip of the minute hand move in 1 hour. (Take π = 3.14)
Q.29 A garden is 90 m long and 75 m broad. A path 5 m wide is to be built outside and around it. Find the area of the path. Also find the area of the garden in hectare.
Q.30 A 3 m wide path runs outside and around a rectangular park of length 125 m and breadth 65m. Find the area of the path.
Q.31 A picture is painted on a cardboard 8 cm long and 5 cm wide such that there is a margin of 1.5 cm along each of its sides. Find the total area of the margin.
Q.33 Pragya wrapped a cord around a circular pipe of radius 4 cm (adjoining figure) and cut off the length required of the cord. Then she wrapped it around a square box of side 4 cm (also shown). Did she have any left? (π = 3.14)
Q.34 The adjoining figure represents a rectangular lawn with a circular flower bed in the middle. Find:
(i) the area of the whole land
(ii) the area of the flower bed
(iii) the area of the lawn excluding the area of the flower bed.
(iv) the circumference of the flower bed.
Q.35 In the following figures, find the area of the shaded portions:
FAQs (Frequently Asked Questions)
You will find the class 7 Mathematics chapter-wise solutions on the Extramarks website.
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Chapter 11 of Class 7 is about Area and Perimeter. Perimeter is the distance around a close figure whereas area is a metric to quantify the region occupied by a figure. Students will learn how to calculate the perimeters and areas of many different shapes including triangles, circles, squares, and parallelograms in this chapter.
Perimeter is the distance that surrounds a specific area whereas, an area is the part of a plane that is encircled by the perimeter. An area is a particular shape that includes a square, rectangle, triangle, etc.
The formula of the area of a circle is πr2.