SUMMARY: The chapter "Perimeter and Area" focuses on understanding and calculating the perimeter and area of various geometric shapes. KEY TOPICS: perimeter of rectangles, perimeter of squares, area of rectangles, area of squares, area of parallelograms, area of triangles, area of circles, units of measurement, conversion of units, real-life applications of perimeter and area.
What is the perimeter of a square with a side length of 5 cm?
A10 cm
B15 cm
C20 cm
D25 cm
Check answerHide answer
Correct answer: Option 3 — 20 cm
Q21 Mark
A rectangle has a length of 8 m and a width of 3 m. What is its area?
A24 m²
B30 m²
C32 m²
D40 m²
Check answerHide answer
Correct answer: Option 1 — 24 m²
Q31 Mark
If the radius of a circle is doubled, how does its area change?
AIt remains the same
BIt doubles
CIt triples
DIt quadruples
Check answerHide answer
Correct answer: Option 4 — It quadruples
Q41 Mark
Calculate the perimeter of a rectangle with a length of 10 cm and a width of 4 cm.
A28 cm
B40 cm
C20 cm
D24 cm
Check answerHide answer
Correct answer: Option 1 — 28 cm
Q51 Mark
A triangle has a base of 6 cm and a height of 4 cm. What is its area?
A12 cm²
B24 cm²
C18 cm²
D30 cm²
Check answerHide answer
Correct answer: Option 1 — 12 cm²
Short Answer Questions5 questions
Q63 Marks
What is the formula to calculate the perimeter of a rectangle? If the length is 8 cm and the width is 5 cm, what is the perimeter?
View sample solutionHide solution
The formula for the perimeter of a rectangle is P = 2(length + width). For a rectangle with a length of 8 cm and a width of 5 cm, the perimeter is P = 2(8 + 5) = 2(13) = 26 cm.
Q73 Marks
Calculate the area of a square with a side length of 6 cm. What is the significance of the area in real-life applications?
View sample solutionHide solution
The area of a square is calculated using the formula A = side × side. For a square with a side length of 6 cm, the area is A = 6 × 6 = 36 cm². The area is significant in real-life applications such as determining the amount of paint needed to cover a wall.
Q83 Marks
Explain how to calculate the area of a triangle. If a triangle has a base of 10 cm and a height of 5 cm, what is its area?
View sample solutionHide solution
The area of a triangle is calculated using the formula A = 1/2 × base × height. For a triangle with a base of 10 cm and a height of 5 cm, the area is A = 1/2 × 10 × 5 = 25 cm².
Q93 Marks
What is the formula for the area of a parallelogram? If the base is 12 cm and the height is 7 cm, what is the area?
View sample solutionHide solution
The formula for the area of a parallelogram is A = base × height. For a parallelogram with a base of 12 cm and a height of 7 cm, the area is A = 12 × 7 = 84 cm².
Q103 Marks
A circular garden has a radius of 3 m. Calculate its area and explain how to convert this area into square centimeters.
View sample solutionHide solution
The area of a circle is calculated using the formula A = π × radius². For a circle with a radius of 3 m, the area is A = π × 3² = 9π m², which is approximately 28.27 m². To convert this area into square centimeters, multiply by 10,000 (since 1 m² = 10,000 cm²), resulting in approximately 282,700 cm².
Long Answer Questions5 questions
Q116 Marks
A rectangular garden has a length of 12 meters and a width of 5 meters. Calculate the perimeter of the garden and explain the steps you took to arrive at your answer.
View sample solutionHide solution
To calculate the perimeter of a rectangle, we use the formula P = 2(length + width). Here, the length is 12 meters and the width is 5 meters. First, we add the length and width: 12 + 5 = 17 meters. Then, we multiply this sum by 2: 2 * 17 = 34 meters. Therefore, the perimeter of the garden is 34 meters.
Q126 Marks
A square park has a side length of 8 meters. Calculate the area of the park and describe how the formula for the area of a square is derived.
View sample solutionHide solution
The area of a square is calculated using the formula A = side × side. In this case, the side length is 8 meters. Therefore, the area is 8 × 8 = 64 square meters. The formula is derived from the fact that a square is made up of equal-length sides, so multiplying the length of one side by itself gives the total area.
Q136 Marks
A triangle has a base of 10 cm and a height of 6 cm. Calculate the area of the triangle and explain how the height is determined in relation to the base.
View sample solutionHide solution
The area of a triangle is calculated using the formula A = 1/2 × base × height. Here, the base is 10 cm and the height is 6 cm. Plugging in these values, we get A = 1/2 × 10 × 6 = 30 square cm. The height is the perpendicular distance from the base to the opposite vertex, ensuring that the area calculation accurately represents the space within the triangle.
Q146 Marks
A circular swimming pool has a radius of 7 meters. Calculate the area of the pool and discuss the significance of using the value of π in your calculations.
View sample solutionHide solution
The area of a circle is calculated using the formula A = π × radius². For a circle with a radius of 7 meters, the area is A = π × 7² = π × 49. Using the approximate value of π as 3.14, we find the area to be approximately 153.86 square meters. The value of π is significant as it represents the ratio of the circumference of a circle to its diameter, and it is essential for accurately calculating areas and circumferences of circular shapes.
Q156 Marks
A parallelogram has a base of 15 cm and a height of 10 cm. Calculate the area of the parallelogram and explain how the area of a parallelogram is similar to that of a rectangle.
View sample solutionHide solution
The area of a parallelogram is calculated using the formula A = base × height. For this parallelogram, the area is A = 15 cm × 10 cm = 150 square cm. The area of a parallelogram is similar to that of a rectangle because both shapes require the base and height for area calculation. In fact, if you were to cut a parallelogram and rearrange it, it could form a rectangle with the same area.
Assertion–Reason Questions5 questions
Q161 Mark
Assertion (A): The perimeter of a square is calculated by multiplying the length of one side by 4.
Reason (R): The perimeter is the total distance around a shape, and for a square, all sides are equal.
Show explanationHide explanation
Correct answer: Option 1 —
Both A and R are true, and R is the correct explanation of A.
Q171 Mark
Assertion (A): The area of a rectangle is found by adding the lengths of all four sides.
Reason (R): The area is calculated by multiplying the length and the width of the rectangle.
Show explanationHide explanation
Correct answer: Option 3 —
A is true, but R is false.
Q181 Mark
Assertion (A): The area of a triangle can be calculated using the formula 1/2 × base × height.
Reason (R): This formula applies to all triangles regardless of their type.
Show explanationHide explanation
Correct answer: Option 1 —
Both A and R are true, and R is the correct explanation of A.
Q191 Mark
Assertion (A): The perimeter of a rectangle is always greater than its area.
Reason (R): The perimeter and area are different measurements and can vary based on the dimensions of the rectangle.
Show explanationHide explanation
Correct answer: Option 4 —
A is false, but R is true.
Q201 Mark
Assertion (A): The area of a circle is calculated using the formula πr^2.
Reason (R): This formula is derived from the relationship between the radius and the area of the circle.
Show explanationHide explanation
Correct answer: Option 1 —
Both A and R are true, and R is the correct explanation of A.
Statement-Based Questions5 questions
Q211 Mark
Statement 1: The perimeter of a rectangle is calculated by adding the lengths of all four sides.
Statement 2: The area of a square is found by multiplying the length of one side by itself.
Show answerHide answer
Correct answer: Option 1 —
Both statements are true.
Q221 Mark
Statement 1: The area of a parallelogram can be calculated using the formula base multiplied by height.
Statement 2: The perimeter of a square is equal to four times the length of its diagonal.
Show answerHide answer
Correct answer: Option 3 —
Only Statement 2 is true.
Q231 Mark
Statement 1: To find the area of a triangle, you can use the formula 1/2 × base × height.
Statement 2: The perimeter of a circle is known as its area.
Show answerHide answer
Correct answer: Option 4 —
Both statements are false.
Q241 Mark
Statement 1: The area of a circle is calculated using the formula πr², where r is the radius.
Statement 2: The perimeter of a rectangle is calculated using the formula 2(length + width).
Show answerHide answer
Correct answer: Option 1 —
Both statements are true.
Q251 Mark
Statement 1: When converting units of measurement, 1 meter is equal to 100 centimeters.
Statement 2: The area of a square is always greater than its perimeter.
Show answerHide answer
Correct answer: Option 2 —
Only Statement 1 is true.
