Class 7 Exam > Class 7 Notes > Mental Math for Class 7 > Mental Maths Questions and Answers: Perimeter and Area
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Page 1
Perimeter and Area
Points to remember
1. Parallelogram:
Perimeter = Sum of all sides
Area = Base × Corresponding height
2. Rectangle:
Perimeter = 2 × Sum of adjacent sides
Or
2 × (length + breadth)
Area = length × breadth
Or
Product of adjacent sides
3. Square:
Perimeter = 4 × side
Area = Side × Side or (???????? )
??
4 Triangle:
Perimeter = Sum of all sides
Area=
?? ?? × Base × Corresponding height
5 Circle:
Circumference (Perimeter) = 2 × p × radius
Area = p × radius × radius or p × (???????????? )
??
Perimeter of regular polygon = No. of sides × Length of one
side
Area of triangle =
?? ?? × Area of parallelogram
Page 2
Perimeter and Area
Points to remember
1. Parallelogram:
Perimeter = Sum of all sides
Area = Base × Corresponding height
2. Rectangle:
Perimeter = 2 × Sum of adjacent sides
Or
2 × (length + breadth)
Area = length × breadth
Or
Product of adjacent sides
3. Square:
Perimeter = 4 × side
Area = Side × Side or (???????? )
??
4 Triangle:
Perimeter = Sum of all sides
Area=
?? ?? × Base × Corresponding height
5 Circle:
Circumference (Perimeter) = 2 × p × radius
Area = p × radius × radius or p × (???????????? )
??
Perimeter of regular polygon = No. of sides × Length of one
side
Area of triangle =
?? ?? × Area of parallelogram
6 Conversion of area units:
Similarly, 1 m
2
= 10000 cm
2
1 Hectare = 10000 m
2
Tricks
? Area of Path-
a) When path is outside the rectangle
Area of path = 2 × (Width of path) × [Length + Breadth of rectangle + 2(Width
of path)]
b) When path is within the rectangle
Area of path = 2 × (Width of path) × [Length + Breadth of rectangle – 2(Width
of path)]
? Area of ring = p × width of ring × [2 × smaller radius + width of ring]
? If the length and breadth of a rectangle is increased by x% and y%
respectively, then area is increased by (x + y +
????
??????
)%
? Area of a square inscribed in a circle of radius r = 2 r
2
? Area of a square circumscribed to a circle of radius r = 4 r
2
? If perimeter of a square is P and Area is A then P = 4vA and A = (
?? ?? )
2
Questions:
1. The circumference of a circle is 154 m, find the diameter.
2. Find the perimeter of a square park, whose area is 625 sq. m.
3. Side of a square is 12 cm. Find its area in sq. cm.
4. If area of ?ABC is 150 sq. cm. and height 6 cm, then find its corresponding
height.
5. If area of a parallelogram is 160 sq. cm. and base is 5 cm, then find its
corresponding height.
6. The length and breadth of a rectangular park are in the ratio 3:2. If the
perimeter of park is 200m, then find its area.
7. If the area of the circle is 154 sq. cm, then find its diameter.
1 cm
2
= 1 cm × 1 cm = 10 mm × 10 mm = 100 mm
2
Page 3
Perimeter and Area
Points to remember
1. Parallelogram:
Perimeter = Sum of all sides
Area = Base × Corresponding height
2. Rectangle:
Perimeter = 2 × Sum of adjacent sides
Or
2 × (length + breadth)
Area = length × breadth
Or
Product of adjacent sides
3. Square:
Perimeter = 4 × side
Area = Side × Side or (???????? )
??
4 Triangle:
Perimeter = Sum of all sides
Area=
?? ?? × Base × Corresponding height
5 Circle:
Circumference (Perimeter) = 2 × p × radius
Area = p × radius × radius or p × (???????????? )
??
Perimeter of regular polygon = No. of sides × Length of one
side
Area of triangle =
?? ?? × Area of parallelogram
6 Conversion of area units:
Similarly, 1 m
2
= 10000 cm
2
1 Hectare = 10000 m
2
Tricks
? Area of Path-
a) When path is outside the rectangle
Area of path = 2 × (Width of path) × [Length + Breadth of rectangle + 2(Width
of path)]
b) When path is within the rectangle
Area of path = 2 × (Width of path) × [Length + Breadth of rectangle – 2(Width
of path)]
? Area of ring = p × width of ring × [2 × smaller radius + width of ring]
? If the length and breadth of a rectangle is increased by x% and y%
respectively, then area is increased by (x + y +
????
??????
)%
? Area of a square inscribed in a circle of radius r = 2 r
2
? Area of a square circumscribed to a circle of radius r = 4 r
2
? If perimeter of a square is P and Area is A then P = 4vA and A = (
?? ?? )
2
Questions:
1. The circumference of a circle is 154 m, find the diameter.
2. Find the perimeter of a square park, whose area is 625 sq. m.
3. Side of a square is 12 cm. Find its area in sq. cm.
4. If area of ?ABC is 150 sq. cm. and height 6 cm, then find its corresponding
height.
5. If area of a parallelogram is 160 sq. cm. and base is 5 cm, then find its
corresponding height.
6. The length and breadth of a rectangular park are in the ratio 3:2. If the
perimeter of park is 200m, then find its area.
7. If the area of the circle is 154 sq. cm, then find its diameter.
1 cm
2
= 1 cm × 1 cm = 10 mm × 10 mm = 100 mm
2
8. A chess board is in square shape as shown in the figure, find the side of each
smaller square.
9. Area of one rectangle is 4800 sq. mm and length of a side is 8 cm, find the other
side.
10. In ?PQR, PL ? QR, PL = 5 cm and QR = 18 cm, find the area of the triangle.
11. If base and height of a parallelogram are 20 cm and 5.5 cm respectively, then
find its area.
12. Find the breadth of the rectangle whose length and breadth are in the ratio 5:3
and perimeter is 48 m.
13. If the ratio of radii of two circles is 6:5, then find the ratio of their
circumferences.
14. A triangle has 19 m base and 6 m corresponding height. Find its area in sq.
cm?
15. In the given figure, find the area of ?LMN with side LQ = 12cm.
Page 4
Perimeter and Area
Points to remember
1. Parallelogram:
Perimeter = Sum of all sides
Area = Base × Corresponding height
2. Rectangle:
Perimeter = 2 × Sum of adjacent sides
Or
2 × (length + breadth)
Area = length × breadth
Or
Product of adjacent sides
3. Square:
Perimeter = 4 × side
Area = Side × Side or (???????? )
??
4 Triangle:
Perimeter = Sum of all sides
Area=
?? ?? × Base × Corresponding height
5 Circle:
Circumference (Perimeter) = 2 × p × radius
Area = p × radius × radius or p × (???????????? )
??
Perimeter of regular polygon = No. of sides × Length of one
side
Area of triangle =
?? ?? × Area of parallelogram
6 Conversion of area units:
Similarly, 1 m
2
= 10000 cm
2
1 Hectare = 10000 m
2
Tricks
? Area of Path-
a) When path is outside the rectangle
Area of path = 2 × (Width of path) × [Length + Breadth of rectangle + 2(Width
of path)]
b) When path is within the rectangle
Area of path = 2 × (Width of path) × [Length + Breadth of rectangle – 2(Width
of path)]
? Area of ring = p × width of ring × [2 × smaller radius + width of ring]
? If the length and breadth of a rectangle is increased by x% and y%
respectively, then area is increased by (x + y +
????
??????
)%
? Area of a square inscribed in a circle of radius r = 2 r
2
? Area of a square circumscribed to a circle of radius r = 4 r
2
? If perimeter of a square is P and Area is A then P = 4vA and A = (
?? ?? )
2
Questions:
1. The circumference of a circle is 154 m, find the diameter.
2. Find the perimeter of a square park, whose area is 625 sq. m.
3. Side of a square is 12 cm. Find its area in sq. cm.
4. If area of ?ABC is 150 sq. cm. and height 6 cm, then find its corresponding
height.
5. If area of a parallelogram is 160 sq. cm. and base is 5 cm, then find its
corresponding height.
6. The length and breadth of a rectangular park are in the ratio 3:2. If the
perimeter of park is 200m, then find its area.
7. If the area of the circle is 154 sq. cm, then find its diameter.
1 cm
2
= 1 cm × 1 cm = 10 mm × 10 mm = 100 mm
2
8. A chess board is in square shape as shown in the figure, find the side of each
smaller square.
9. Area of one rectangle is 4800 sq. mm and length of a side is 8 cm, find the other
side.
10. In ?PQR, PL ? QR, PL = 5 cm and QR = 18 cm, find the area of the triangle.
11. If base and height of a parallelogram are 20 cm and 5.5 cm respectively, then
find its area.
12. Find the breadth of the rectangle whose length and breadth are in the ratio 5:3
and perimeter is 48 m.
13. If the ratio of radii of two circles is 6:5, then find the ratio of their
circumferences.
14. A triangle has 19 m base and 6 m corresponding height. Find its area in sq.
cm?
15. In the given figure, find the area of ?LMN with side LQ = 12cm.
16. From the given figure, find the area of ? ABC,
17. If length of a rectangle is 12 cm and area is 108 sq. cm, then find the perimeter.
18. If the ratio of radii of two circles is 3:5, then find the ratio of their areas.
19. Area of a circle is 1540000 sq. cm. find the radius.
20. For making a paper envelope, a rectangular paper of 15 cm × 12 cm is
required. Find the total cost of 5 such envelopes at 2 paisa per sq. cm.
21. If radius of a wheel is 7 m, find the distance covered in 15 revolutions.
22. Length and breadth of a garden is 300 m and 200 m respectively, find its area
in hectares?
23. Find the length of the rectangle whose breadth is 20 cm and perimeter is 90
cm.
24. A strip is cut around one rectangular sheet. Find the remaining area.
25. Find the perimeter of the given semicircular shape.
Page 5
Perimeter and Area
Points to remember
1. Parallelogram:
Perimeter = Sum of all sides
Area = Base × Corresponding height
2. Rectangle:
Perimeter = 2 × Sum of adjacent sides
Or
2 × (length + breadth)
Area = length × breadth
Or
Product of adjacent sides
3. Square:
Perimeter = 4 × side
Area = Side × Side or (???????? )
??
4 Triangle:
Perimeter = Sum of all sides
Area=
?? ?? × Base × Corresponding height
5 Circle:
Circumference (Perimeter) = 2 × p × radius
Area = p × radius × radius or p × (???????????? )
??
Perimeter of regular polygon = No. of sides × Length of one
side
Area of triangle =
?? ?? × Area of parallelogram
6 Conversion of area units:
Similarly, 1 m
2
= 10000 cm
2
1 Hectare = 10000 m
2
Tricks
? Area of Path-
a) When path is outside the rectangle
Area of path = 2 × (Width of path) × [Length + Breadth of rectangle + 2(Width
of path)]
b) When path is within the rectangle
Area of path = 2 × (Width of path) × [Length + Breadth of rectangle – 2(Width
of path)]
? Area of ring = p × width of ring × [2 × smaller radius + width of ring]
? If the length and breadth of a rectangle is increased by x% and y%
respectively, then area is increased by (x + y +
????
??????
)%
? Area of a square inscribed in a circle of radius r = 2 r
2
? Area of a square circumscribed to a circle of radius r = 4 r
2
? If perimeter of a square is P and Area is A then P = 4vA and A = (
?? ?? )
2
Questions:
1. The circumference of a circle is 154 m, find the diameter.
2. Find the perimeter of a square park, whose area is 625 sq. m.
3. Side of a square is 12 cm. Find its area in sq. cm.
4. If area of ?ABC is 150 sq. cm. and height 6 cm, then find its corresponding
height.
5. If area of a parallelogram is 160 sq. cm. and base is 5 cm, then find its
corresponding height.
6. The length and breadth of a rectangular park are in the ratio 3:2. If the
perimeter of park is 200m, then find its area.
7. If the area of the circle is 154 sq. cm, then find its diameter.
1 cm
2
= 1 cm × 1 cm = 10 mm × 10 mm = 100 mm
2
8. A chess board is in square shape as shown in the figure, find the side of each
smaller square.
9. Area of one rectangle is 4800 sq. mm and length of a side is 8 cm, find the other
side.
10. In ?PQR, PL ? QR, PL = 5 cm and QR = 18 cm, find the area of the triangle.
11. If base and height of a parallelogram are 20 cm and 5.5 cm respectively, then
find its area.
12. Find the breadth of the rectangle whose length and breadth are in the ratio 5:3
and perimeter is 48 m.
13. If the ratio of radii of two circles is 6:5, then find the ratio of their
circumferences.
14. A triangle has 19 m base and 6 m corresponding height. Find its area in sq.
cm?
15. In the given figure, find the area of ?LMN with side LQ = 12cm.
16. From the given figure, find the area of ? ABC,
17. If length of a rectangle is 12 cm and area is 108 sq. cm, then find the perimeter.
18. If the ratio of radii of two circles is 3:5, then find the ratio of their areas.
19. Area of a circle is 1540000 sq. cm. find the radius.
20. For making a paper envelope, a rectangular paper of 15 cm × 12 cm is
required. Find the total cost of 5 such envelopes at 2 paisa per sq. cm.
21. If radius of a wheel is 7 m, find the distance covered in 15 revolutions.
22. Length and breadth of a garden is 300 m and 200 m respectively, find its area
in hectares?
23. Find the length of the rectangle whose breadth is 20 cm and perimeter is 90
cm.
24. A strip is cut around one rectangular sheet. Find the remaining area.
25. Find the perimeter of the given semicircular shape.
26. Find the shaded area in the adjoining figure
27. If the area of a triangle is equal to the area of a square of side 12 cm, height is
18 cm, then find the corresponding side.
28. A wire bent in the form of rectangle with length 65 cm and breadth 35 cm. If
it is re-bent in the form of a square, then find the area of square.
29. A square carpet of side 10 m is laid on a rectangular floor with dimensions 12
m × 10 m, find area of the floor which is not carpeted?
30. Find the shaded area in the adjoining figure.
31. Find the area of ?RSQ in the adjoining figure.
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FAQs on Mental Maths Questions and Answers: Perimeter and Area - Mental Math for Class 7
| 1. What is the formula for calculating the perimeter of a rectangle? |  |
Ans. The formula for calculating the perimeter of a rectangle is P = 2(l + w), where l is the length and w is the width of the rectangle.
| 2. How do you find the area of a square? | |
Ans. To find the area of a square, you can use the formula A = side x side, where side is the length of one side of the square.
| 3. Can the perimeter of a rectangle be equal to its area? | |
Ans. No, the perimeter of a rectangle and its area are two different measurements. The perimeter is the distance around the outside of the rectangle, while the area is the space inside the rectangle.
| 4. How do you calculate the area of a triangle? | |
Ans. The formula for calculating the area of a triangle is A = 0.5 x base x height, where the base is the length of the triangle's base and the height is the perpendicular distance from the base to the opposite vertex.
| 5. Is the perimeter of a shape always greater than its area? | |
Ans. Not necessarily. The perimeter and area of a shape are independent of each other, so it is possible for the area to be greater than the perimeter depending on the dimensions of the shape.
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Mental Maths Questions and Answers: Perimeter and Area Class 7
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