SECTION A – MCQs
- The area of a rectangle with length 20 cm and width 8 cm is:
(a) 120 cm² (b) 160 cm² (c) 180 cm² (d) 200 cm² - A square has side 15 cm. Its perimeter is:
(a) 45 cm (b) 50 cm (c) 60 cm (d) 75 cm - A circle with radius 7 cm has circumference:
(Use π = 22/7)
(a) 22 cm (b) 44 cm (c) 33 cm (d) 66 cm - The area of a triangle with base 12 cm and height 5 cm is:
(a) 30 cm² (b) 60 cm² (c) 24 cm² (d) 12 cm² - Perimeter of a square is 80 cm. Its side is:
(a) 10 cm (b) 20 cm (c) 15 cm (d) 25 cm - A parallelogram has base 14 cm and height 9 cm. Area =
(a) 108 cm² (b) 126 cm² (c) 72 cm² (d) 140 cm² - Diameter of a circle is 18 cm. Radius is:
(a) 6 cm (b) 9 cm (c) 12 cm (d) 3 cm - 1 hectare =
(a) 100 m² (b) 1000 m² (c) 10,000 m² (d) 1,000,000 m² - The length of a rectangle is twice its breadth. If its area is 128 cm², its breadth is:
(a) 4 cm (b) 8 cm (c) 10 cm (d) 16 cm - The area of a circle with radius 3 cm is:
(a) 6π cm² (b) 9π cm² (c) 3π cm² (d) 12π cm² - Perimeter of a triangle with sides 5 cm, 12 cm, 13 cm:
(a) 30 cm (b) 25 cm (c) 22 cm (d) 35 cm - A square and a rectangle have equal perimeter. Which has larger area?
(a) Square (b) Rectangle (c) Both same (d) None - The circumference of a circle increases if:
(a) radius decreases (b) radius doubles (c) radius is half (d) radius is zero - The area of a square is 196 m². Side =
(a) 12 m (b) 14 m (c) 16 m (d) 18 m - Area of a parallelogram with base 20 cm and height 3 cm is:
(a) 23 cm² (b) 40 cm² (c) 60 cm² (d) 80 cm² - A circle with circumference 31.4 cm has radius:
(Use π = 3.14)
(a) 5 cm (b) 6 cm (c) 3 cm (d) 4 cm - Area of right triangle with legs 9 cm and 12 cm:
(a) 54 cm² (b) 108 cm² (c) 36 cm² (d) 45 cm² - Area of square of side 2.5 m:
(a) 6.25 m² (b) 10 m² (c) 12.5 m² (d) 2.5 m² - Perimeter of regular pentagon with side 9 cm =
(a) 36 cm (b) 27 cm (c) 45 cm (d) 54 cm - A triangle has area 49 cm² and base 7 cm. Height =
(a) 10 cm (b) 12 cm (c) 14 cm (d) 18 cm
SECTION B – Fill in the blanks
- Area of a square = ________.
- Circumference of a circle = ________.
- If perimeter = 2(l + b), l = 10 and b = 5, perimeter = ________.
- The distance around a circle is called its ________.
- A parallelogram has area = base × ________.
- Radius = half of the ________.
- 10000 cm² = ________ m²
- The area of triangle = ________ × base × height.
- A circle with diameter 10 cm has radius ________.
- Perimeter of square = ________ × side.
Section C – Very Short Numericals
Solve and give final answer with units.
- Find the area of a rectangle of length 18 cm and breadth 7 cm.
- A square has side 11 cm. Find its perimeter.
- A triangle has base 12 cm and height 8 cm. Find its area.
- The radius of a circle is 5 cm. Find its circumference. (Take π = 3.14)
- The area of a square is 144 m². Find its side.
- A rectangle has area 96 cm² and breadth 8 cm. Find its length.
- The circumference of a circle is 31.4 cm. Find the radius. (π = 3.14)
- A parallelogram has base 15 cm and height 6 cm. Find its area.
- Convert 8,000 cm² into m².
- The perimeter of a rectangle is 50 cm and its length is 15 cm. Find its breadth.
Section D – Short Numericals
Show steps clearly.
- A rectangular garden is 25 m long and 18 m wide.
(a) Find its perimeter.
(b) Find its area. - A square plot has a perimeter of 84 m.
(a) Find the side of the plot.
(b) Find its area. - The area of a rectangular sheet is 360 cm². If its length is 24 cm, find:
(a) its breadth
(b) its perimeter. - The base of a triangle is 20 cm and its height is 13 cm. Find the area of the triangle.
- A parallelogram has an area of 150 cm² and base 25 cm. Find the height of the parallelogram.
- Find the area and circumference of a circle whose radius is 7 cm. (Take π = 22/7)
- A square field has area 484 m².
(a) Find the side of the field.
(b) Find its perimeter. - A wire of length 48 cm is bent to form a square.
(a) Find the length of each side.
(b) Find the area of the square. - The diameter of a circular park is 28 m.
(a) Find its radius.
(b) Find its area. (Take π = 22/7) - A room floor is 12 m long and 9 m wide. Tiles of size 1 m × 1 m are used.
(a) Find the area of the floor.
(b) Find the number of tiles required to cover the floor.
Section E – Long Numericals
Draw figures wherever needed and show full working.
- A path 2 m wide is built all around a rectangular park of length 40 m and breadth 26 m.
(a) Find the area of the park.
(b) Find the area of the park including the path.
(c) Find the area of the path. - A circular garden has a radius of 14 m. Around it, a path 3 m wide is made.
(a) Find the outer radius of the circular region.
(b) Find the area of the path. (Take π = 22/7) - A wire of length 88 cm is first bent into a rectangle of length 30 cm.
(a) Find the breadth of the rectangle.
(b) Find the area of the rectangle.
Then the same wire is bent to form a circle.
(c) Find the radius of the circle.
(d) Find the area of the circle. (Take π = 22/7) - A rectangular field is 60 m long and 35 m wide. A path 2.5 m wide runs inside the field along all four sides.
(a) Find the area of the whole field.
(b) Find the area of the inner rectangle (without path).
(c) Find the area of the path. - The minute hand of a clock is 10 cm long.
(a) Find the distance travelled by the tip of the minute hand in 1 hour.
(b) Find the distance travelled by the tip in 6 hours. (Take π = 22/7) - A farmer has a square field of side 50 m. He wants to fence it with 3 rounds of wire.
(a) Find the perimeter of the field.
(b) Find the total length of wire needed for 3 rounds.
(c) If each metre of wire costs ₹12, find the total cost of the wire. - A circular flower bed of radius 6 m is in the middle of a square lawn of side 20 m.
(a) Find the area of the square lawn.
(b) Find the area of the flower bed.
(c) Find the area of the lawn excluding the flower bed. (Take π = 3.14) - The diameter of a wheel is 70 cm.
(a) Find the circumference of the wheel. (Take π = 22/7)
(b) How many revolutions will the wheel make to cover a distance of 2.2 km? - In the figure, ABCD is a square with each side measuring 14 cm. Draw four circles using A, B, C and D as centres, ensuring that each circle touches two of the other circles externally. Calculate the area of the shaded region.
- Calculate the shaded region’s area for every figure shown.
- Calculate the area of each triangle shown below.
- A paper sheet is shaped like a rectangle ABCD with AB = 18 cm and BC = 14 cm. A semicircle is cut out from the sheet using BC as the diameter. Calculate the area of the paper that remains after removing the semicircle.
