Find the area of the rectangle whose dimensions are:
(i) Length = 24.5 m, breadth = 18m
(ii) Length = 12.5 m, breadth = 8dm
The sides of a rectangular park are in the ratio 4:3. If its area is 1728 \mathrm{m}^{2}, find the cost of fencing it at ₹ 30 per meter.
The cost of carpeting a room 15 m long with a carpet of width 75 cm at ₹ 80 per meter is ₹ 19200. Find the width of the room.
Find the length of the largest pole that can be placed in a hall 10 m long, 10 m wide and 5 m high.
A rectangle plot of land measures 95 m by 72 m. Inside the plot, a path of uniform width of 3.5 m is to be constructed all around. He rest of the plot is to be laid with grass. Find the total expenses involved in constructing the path at ₹ 80per m^{2} and laying the grass at ₹ 40 per\mathrm{m}^{2}.
A rectangular grassy lawn measuring 38 m by 25 m has been surrounded externally by a 2.5-m wide path. Calculate the cost of graveling the path at the rate of ₹ 120 per\mathrm{m}^{2}.
Each side of a square flower bed is 2 m 80 cm long. It is extended by digging a strip 30 cm wide all around it. Find the area of the enlarged flower bed and also the increase in the area of the flower bed.
A school has a hall which is 22 m long and 15.5 m broad. A carpet is laid inside the hall leaving all-around a margin of 75 cm from the walls. Find the area of the carpet and the area of the strip left in uncovered. If the width of the carpet is 82 cm, find its cost at the rate of ₹ 60 per m.
Find the area of a parallelogram with base 32 cm and height 16.5 cm.
The base of a parallelogram measures 1 m 60 cm and its height is 75 cm. Find its area in \mathrm{m}^{2}.
Find the height of a parallelogram whose area is 54 \mathrm{cm}^{2} and the base is 15 cm.
One side of a parallelogram is 18 cm long and its area is 153 \mathrm{cm}^{2}. Find the distance of the given side from its opposite side.
In a parallelogram ABCD, AB = 18 cm, BC = 12 cm, AL ⊥ DC and AM ⊥ BC.
If AL = 6.4 cm, find the length of AM.
Find the area of the triangle in which
(i) base = 42 cm and height = 25 cm.
(ii) base = 16.8 m and height = 75 cm.
(iii) base = 8 dm and height = 35 cm.
Find the height of the triangular region having an area of 224 \mathrm{m}^{2} and base 28 m.
The base of a triangular field is three times its height. If the cost of cultivating the field at ₹ 1080 per hectare is ₹ 14580, find its base and height.
Find the area of a right triangle whose base is 1.2 m and hypotenuse 3.7 m.
The legs of a right triangle are in the ratio 3: 4 and its area is 1014 \mathrm{cm}^{2}. Find the lengths of its legs.
The area of an equilateral triangle is (16 × √3) \mathrm{cm}^{2}. Find the length of each side of the triangle.
Find the circumference of a circle whose diameter is
(i) 35 cm, (ii) 4.9 m
The ratio of the radii of two circles is 5: 3. Find the ratio of their circumferences.
A racetrack is in the form of a ring whose inner circumference is 528 m and the outer circumference is 616 m. Find the width of the track.
The inner circumference of a circular track is 330 m. The track is 10.5 m wide everywhere. Calculate the cost of putting up a fence along the outer circle at the rate of ₹ 20 per meter.
Find the area of a circle whose radius is
(i) 21 cm, (ii) 3.5 m
Find the area of a circle whose diameter is
(i) 28 cm, (ii) 1.4m
The circumference of a circle is 264 cm. Find its area.
The circumference of a circle is 35.2 m. Find its area.
The area of a circle is 616 \mathrm{cm}^{2}. Find its circumference.
The area of a circle is 1386 \mathrm{m}^{2}. Find its circumference.
The ratio of the radii of two circles is 4: 5. Find the ratio of their areas.
A horse is tied to a pole in a park with a string 21 m long. Find the area over which the horse can graze.
Mark against the correct answer in the following:
The length of a rectangle is 16 cm and the length of its diagonal is 20 cm. The area of the rectangle
is
(a) 320 \mathrm{cm}^{2} (b) 160 \mathrm{cm}^{2} (c) 192 \mathrm{cm}^{2} (d) 156 \mathrm{cm}^{2}
Each diagonal of a square is 12 cm long. Its area is
(a) 144 \mathrm{cm}^{2} (b) 72 \mathrm{cm}^{2} (c) 36 \mathrm{cm}^{2} (d) none of these
The area of a square is 200 \mathrm{cm}^{2}. The length of its diagonal is
(a) 10 cm (b) 20 cm (c) 10√2 cm (d) 14.1 cm
The area of a square field is 0.5 hectare. The length of its diagonal is
(a) 100 m (b) 50 m (c) 250 m (d) 50√2 m
The length of a rectangular field is thrice its breadth and its perimeter is 240 m. The length of the field is
(a) 80 m (b) 120 m (c) 90 m (d) none of these
On increasing each side of a square by 25 %, the increase in area will be
(a) 25% (b) 55% (c) 40.5% (d) 56.25%
The area of a square and that of a square drawn on its diagonal are in the ratio
(a) 1: √2 (b) 1: 2 (c) 1: 3 (d) 1: 4
The perimeters of a square and a rectangle are equal. If their areas be A m^{2} \text { and } B m^{2}, then which
of the following is a true statement?
(a) A < B (b) A \leq B (c) A > B (d) A \geq B
The length and breadth of a rectangular field are in the ratio 5: 3 and its perimeter is 480 m. The area of the field is
(a) 7200 \mathrm{m}^{2} (b) 13500 \mathrm{m}^{2} (c) 15000 \mathrm{m}^{2} (d) 540000 \mathrm{m}^{2}
The length of a room is 15 m. the cost of carpeting it with a carpet 75 cm wide at ₹ 50 per meter is ₹ 6000. The width of the room is
(a) 6 m (b) 8 m (c) 13.4 m (d) 18 m
The sides of a triangle measures 13 cm, 14 cm and 15 cm. Its area is
(a) 84 \mathrm{cm}^{2} (b) 91 \mathrm{cm}^{2} (c) 168 \mathrm{cm}^{2} (d) 182 \mathrm{cm}^{2}
The base and height of a triangle is are 12 m and 8 m respectively. Its area is
(a) 96 \mathrm{m}^{2} (b) 48 \mathrm{m}^{2} (c) 16√3\mathrm{m}^{2} (d) 16√2\mathrm{m}^{2}
The area of an equilateral triangle is 4√3 \mathrm{cm}^{2}. The length of each of its sides is
(a) 3 cm (b) 4 cm (b) 2√3 cm (d) ½ √3 cm
Each side of an equilateral triangle is 8 cm long. Its area is
(a) 32 \mathrm{cm}^{2} (b) 64 \mathrm{cm}^{2} (c) 16√3 \mathrm{cm}^{2} (d) 16√2 \mathrm{cm}^{2}
The height of an equilateral triangle is √6 cm. Its area is
(a) 3√3 \mathrm{cm}^{2} (b) 2√3 \mathrm{cm}^{2} (c) 2√2 \mathrm{cm}^{2} (d) 6√2 \mathrm{cm}^{2}
One side of a parallelogram is 16 cm and the distance of this side from the opposite side is 4.5 cm. The area of the parallelogram is
(a) 36 \mathrm{cm}^{2} (b) 72 \mathrm{cm}^{2} (c) 18 \mathrm{cm}^{2} (d) 54 \mathrm{cm}^{2}
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