The Class 9 Maths Chapter 6 Measuring Space: Perimeter and Area Worksheet with Answers PDF helps students practice questions based on the measurement of different geometrical shapes. This CBSE Board, NCERT chapter focuses on calculating the perimeter and area of squares, rectangles, triangles, circles, parallelograms, and composite figures using suitable formulas. Students learn how these concepts are applied to measure space in mathematical problems and real-life situations.
In Ganita Manjari Chapter 6, students understand important formulas, including area formulas, perimeter formulas, and Heron’s formula for triangles. This worksheet provides basic questions, concept-based problems, and application-level exercises with step-by-step solutions to improve accuracy and problem-solving skills.
These Worksheets are useful for regular revision, homework practice, and exam preparation. Students searching for Class 9 Worksheets can use this chapter-wise resource to build a stronger understanding of geometry concepts. The Class 9 Maths Worksheets are designed to make formula application easier and help students solve different types of measurement-based questions confidently.
Download Class 9 Measuring Space: Perimeter and Area Worksheet PDF with Answers
Students can download the Chapter 6 Measuring Space: Perimeter and Area Maths Worksheet PDF to practice different types of questions. This worksheet contains important problems with detailed solutions to help students understand formulas and their applications.
Download Measuring Space: Perimeter and Area Chapter 6 Class 9 Worksheet PDF
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Class 9 Measuring Space: Perimeter and Area Worksheet Questions
Basic Questions
Question 1:
Find the perimeter of a square whose side length is 12 cm.
Question 2:
Calculate the area of a rectangle with length 15 m and breadth 8 m.
Question 3:
Find the circumference of a circle having radius 7 cm.
(Take π = 22/7)
Question 4:
Write the formula for finding the area of a triangle when its base and height are given.
Question 5:
A square has an area of 81 cm². Find the length of its side.
Concept Questions
Question 6:
If the side of a square becomes three times its original length, how many times will its area increase?
Question 7:
The sides of a triangle are 5 cm, 12 cm, and 13 cm. Find its area using Heron’s formula.
Question 8:
A wire of length 44 cm is bent into a circular shape. Find the radius of the circle formed.
(Take π = 22/7)
Question 9:
The ratio of the circumference of two circles is 4:7. Find the ratio of their radii.
Question 10:
Find the area of a parallelogram having base 18 cm and height 9 cm.
Application Questions
Question 11:
A rectangular garden has an area of 600 m². If its length is 30 m, calculate its breadth and perimeter.
Question 12:
A parallelogram-shaped field has a base of 20 m and height of 15 m. If the cost of covering the field is ₹25 per m², find the total cost.
Question 13:
A square sheet has a diagonal length of 20 cm. Find the area of the square.
Question 14:
A circular park has radius 14 m. Find the area covered by the park.
(Take π = 22/7)
Question 15:
A trapezium has parallel sides of 30 cm and 18 cm. Its height is 10 cm. Calculate the area of the trapezium.
Class 9 Measuring Space: Perimeter and Area Worksheet Answer Key with Solutions
Answer 1:
Perimeter of square = 4 × side
= 4 × 12
= 48 cm
Answer 2:
Area of rectangle = length × breadth
= 15 × 8
= 120 m²
Answer 3:
Circumference of circle = 2πr
= 2 × 22/7 × 7
= 44 cm
Answer 4:
Area of triangle:
= 1/2 × base × height
Answer 5:
Area of square = side²
81 = side²
Side = √81
= 9 cm
Answer 6:
Original side = a
Original area = a²
New side = 3a
New area = (3a)² = 9a²
The area becomes 9 times the original area.
Answer 7:
Given sides:
a = 5 cm
b = 12 cm
c = 13 cm
Semi-perimeter:
s = (5 + 12 + 13) / 2
s = 15 cm
Using Heron’s Formula:
Area = √s(s-a)(s-b)(s-c)
= √15(15-5)(15-12)(15-13)
= √(15 × 10 × 3 × 2)
= √900
= 30 cm²
Answer 8:
Circumference = 44 cm
2πr = 44
2 × 22/7 × r = 44
r = 7 cm
Answer 9:
Circumference of circle = 2πr
Since 2π is constant,
Ratio of circumferences = Ratio of radii
Therefore, radius ratio = 4 : 7
Answer 10:
Area of parallelogram:
= base × height
= 18 × 9
= 162 cm²
Answer 11:
Area of rectangle = length × breadth
600 = 30 × breadth
Breadth = 20 m
Perimeter:
= 2(length + breadth)
= 2(30 + 20)
= 100 m
Answer 12:
Area of field:
= 20 × 15
= 300 m²
Total cost:
= 300 × 25
= ₹7500
Answer 13:
For a square:
Diagonal² = side² + side²
20² = 2 × side²
400 = 2 × side²
side² = 200
Area of square = side²
= 200 cm²
Answer 14:
Area of circle:
= πr²
= 22/7 × 14 × 14
= 616 m²
Answer 15:
Area of trapezium:
= 1/2 × (sum of parallel sides) × height
= 1/2 × (30 + 18) × 10
= 24 × 10
= 240 cm²
Concepts Covered in Measuring Space: Perimeter and Area Worksheet
The chapter 6 Measuring Space Perimeter and Area Maths worksheet questions cover the following concepts:
| Concept | Learning Area |
|---|---|
| Perimeter | Finding boundary length of closed figures |
| Area | Measuring space covered by shapes |
| Square and Rectangle | Using length, breadth, and side formulas |
| Triangle | Area calculation and Heron’s formula |
| Circle | Radius, circumference, and area |
| Parallelogram | Base and height-based calculations |
| Trapezium | Area of figures with parallel sides |
| Composite Figures | Breaking complex shapes into simple parts |
Learning Outcomes After Solving Measuring Space: Perimeter and Area Worksheet
After completing the Chapter 6 Measuring Space: Perimeter and Area Maths Worksheet, students will be able to:
- Identify suitable area and perimeter formulas for different shapes.
- Calculate measurements of squares, rectangles, circles, and triangles.
- Apply Heron’s formula to find the area of triangles.
- Solve geometry questions based on real-life situations.
- Understand the relationship between dimensions and area changes.
- Improve mathematical reasoning through step-by-step solutions.
- Build confidence in solving Class 9 geometry problems.
