Frank solutions for Mathematics [English] Class 9 ICSE chapter 24 - Perimeter and Area [Latest edition]

Find the area of a triangle whose base is 3.8 cm and height is 2.8 cm.

Find the area of a triangle whose sides are 27 cm, 45 cm and 36 cm.

Find the area of an isosceles triangle ABC in which AB = AC = 6 cm, ∠A = 90°. Also, find the length of perpendicular from A to BC.

Find the area of an equilateral triangle of side 20 cm.

Find the perimeter of an equilateral triangle whose area is `16sqrt(3)"cm"`.

Find the area of an equilateral triangle having perimeter of 18cm.

Find the area of a triangle whose sides are in the ratio 5:12:13 and whose perimeter is 36cm.

The perimeter of a triangle is 72cm and its sides are in the ratio 3:4:5. Find its area and the length of the altitude corresponding to the longest side.

Find the area of a right angled triangle whose hypotenuse is 15cm and the base is 9cm.

Find the area of the shaded region in the figure as shown, in which DPQS is an equilateral triangle and ∠PQR = 90°.

The area of an equilateral triangle is numerically equal to its perimeter. Find the length of its sides, correct two decimal places.

In a right-angled triangle PQR right-angled at Q, QR = x cm, PQ = (x + 7) cm and area = 30 cm². Find the sides of the triangle.

In a right-angled triangle ABC, if ∠B = 90°, AB - BC = 2 cm; AC - BC = 4 and its perimeter is 24 cm, find the area of the triangle.

In a right-angled triangle ABC, if ∠B = 90°, AB - BC = 2 cm; AC - BC = 4 and its perimeter is 24 cm, find the area of the triangle.

Find the area of an isosceles triangle whose perimeter is 50cm and the base is 24cm.

Find the area of an isosceles triangle whose perimeter is 72cm and the base is 20cm.

The base of a triangle field and its height are in the ratio 2:5. If the cost of cultivating the field at Rs.42 per sq. m is Rs.7560, find its base and height.

The cost of fencing a triangular field at the rate of Rs.15 per m is Rs.900. If the lengths of the triangle are in the ratio 3:4:5, find the area of the triangle and the cost of cultivating it at Rs.48 per kg sq.m.

Find the area of a triangle with a base 12cm and a height equal to the width of a rectangle having area of 96cm² and a length of 12cm.

Find the base of an isosceles triangle whose area is 192cm² and the length of one of the equal sides is 20cm.

Each equal side of an isosceles triangle is 3cm less than the unequal side. The height of the perpendicular from the vertex to the unequal side is 3cm less than the equal side. If the area of the isosceles triangle is 108cm², find the perimeter of the triangle.

The side of a square is of length 20 mm. Find its perimeter in cm.

The area of a square is 36 cm². How long are its sides?

The sides of a rectangle are 5 cm and 3 cm respectively. Find its area in mm².

Find the area and perimeter of the given figure.

Find the shaded area in the given figure.

Find the area of each of the following figure:

Find the area of each of the following figure:

Find the area of each of the following figure:

Find the area of each of the following figure:

Find the area of a parallelogram whose base is 12cm and the height is 5cm.

Find the height of a parallelogram whose area is 144cm² and the base is 18cm.

Find the area of quadrilateral, whose diagonals of lengths 18 cm and 13 cm intersect each other at right angle.

In a rectangle ABCD, AB = 7 cm and AD = 25 cm. Find the height of a triangle whose base is AB and whose area is two times the area of the rectangle ABCD.

Two adjacent sides of a parallelogram are 34 cm and 20 cm. If one of its diagonal is 42 cm, find: area of the parallelogram.

Two adjacent sides of a parallelogram are 34 cm and 20 cm. If one of its diagonal is 42 cm, find: distance between its shorter sides

One side of a parallelogram is 12cm and the altitude corresponding to i is 8cm. If the length of the altitude corresponding to its adjacent side is 16cm, find the length of the adjacent side.

Two adjacent sides of a parallelogram are 20cm and 18cm. If the distance between the larger sides is 9cm, find the area of the parallelogram. Also, find the distance between the shorter sides.

Find the perimeter and area of a rectangle whose length and breadth are 12cm and 9cm respectively.

The area of a floor of a rectangular room is 360m². If its length is 24cm, find its perimeter.

The length of a rectangular field is thrice of its width. If the perimeter of this field is 1.6km, find its area in sq.m.

A rectangular field 240m long has an area 36000m². Find the cost of fencing the field at Rs.2.50per m.

In a trapezium the parallel sides are 12cm and 8cm. If the distance between them is 6cm, find the area of the trapezium.

A rectangular floor 45 in long and 12 m broad is to be paved exactly with square tiles, of side 60 cm. Find the total number of tiles required to pave it.
If a carpet is laid on the floor such as a space of 50 cm exists between its edges and the edges of the floor, find what fraction of the floor is uncovered.

A rectangular hall of 40m by 24m is covered with carpets of size 6m x 4m. Find the number of carpets required to cover the hall.

The area of a square garden is equal to the area of a rectangular plot of length 160m and width 40m. Calculate the cost of fencing the square garden at Rs.12per m.

Find the area of a square whose diagonal is `12sqrt(12)"cm"`

Find the perimeter and area of a square whose diagonal is `5sqrt(2)"cm"`. Give your answer correct to two decimal places if `sqrt(2)` = 1.414.

Find the perimeter of a rhombus whose diagonals are 24cm and 10cm.

The perimeter of a square plot of land is 64m. The area of a nearby rectangular plot is 24m² more than the area of the given square. If the length of the rectangle is 14m, find its breadth.

The perimeter of a square is 128cm and that of another is 96cm. Find the perimeter and the diagonal of a square whose area is equal to the sum of the areas of these two squares.

The area of a square plot of side 80m is equal to the area of a rectangular plot of length 160m. Calculate the width of the rectangular plot and the cost of fencing it Rs.7.50per m.

The side of a square exceeds the side of another square by 4cm and the sum of the areas of the squares is 400cm². Find the dimensions of the squares.

Find the area of a rhombus, whose one side and one diagonal measure 20cm and 24cm respectively.

The area of a rhombus is 234 cm². If its one diagonal is 18 cm, find the lengths of its side and the other diagonal. Also, find perimeter of the rhombus.

Find the area of a rhombus whose perimeter is 260cm and the length of one of its diagonal is 66cm.

A rectangular field is 80m long and 50m wide. A 4m wide runs through the centre of the field parallel to the length and breadth of the field. Find the total area of the roads.

A quadrilateral field of unequal has a longer diagonal with 140m. The perpendiculars from opposite vertives upon this diagonal are 20m and 14m. Find the area of the field.

A lawn in the shape of a rectangle is to be developed in front of a Marriage Hall. The length and breadth of the lawn are 44m and 32m. A space of 2m is left on the two shoulder sides and one longer side for flower and in the remaining area grass is laid. Calculate the area of the flower space and the area on which grass is laid.

The floor of a room is of size 6 m x 5 m. Find the cost of covering the floor of the room with 50 cm wide carpet at the rate of Rs.24.50 per metre. Also, find the cost of carpeting the same hall if the carpet, 60 cm, wide, is at the rate of Rs.26 per metre.

A rectangular field is 240m long and 180m broad. In one corner a farm house is built on a square plot of side 40m. Find the area of the remaining portion and the cost of fencing the open sides Rs.25per m.

Inside a square field of side 44m, a square flower bed is prepared leaving a graved path all round the flower bed. The total cost of laying the flower bed at Rs.25per  sq m. and gravelling the path at Rs.120per sq m. is Rs.80320. Find the width of the gravel path.

The length and breadth of a rectangular field are in the ratio 8 : 5. A 2m wide path runs all around outside the field. The area of the path is 848m². Find the length and breadth of the field.

A footpath of uniform width runs all around the inside of a rectangular garden of 40 m x 30 m. If the path occupies 136 m², find the width of the path.

How many tiles, each of area 625 cm², will be needed to pave a footpath which is 1 m wide and surrounds a grass plot of size 38 m x 14 m?

PQRS is a square with each side 6cm. T is a point on QR such that the `"area of ΔPQT"/"area of trapezium PTRS" = (1)/(3)` Find the length of TR.

The perimeter of a rectangular plot is 300m. It has an area of 5600m². Taking the length of the plot as x m, calculate the breadth of the plot in terms of x, form an equation and solve it to find the dimensions of the plot.

Find the area of a quadrilateral field whose sides are 12m, 9m, 18m and 21m respectively and the angle between the first two sides is a right angle. Take the value of `sqrt(6)` as 2.5.

Find the diagonal of a quadrilateral whose area is 756cm² and the perpendicular from the opposite vertices are 17cm and 19cm.

A wire when bent in the form of a square encloses an area of 16 cm². Find the area enclosed by it when the same wire is bent in the form of a rectangle whose sides are in the ratio of 1 : 3

A wire when bent in the form of a square encloses an area of 16 cm². Find the area enclosed by it when the same wire is bent in the form of an equilateral triangle

A chessboard contains 64 equal square and the area of each square is 6.25cm². A 2cm wide border is left inside of the board. Find the length of the side of the chessboard.

The cross-section of a canal is a trapezium in shape. If the canal is 10m wide at the top, 6m wide at the bottom and the area of cross-section is 72 sq.m, determine its depth.

Find the area and perimeter of the circles with following: Radius = 2.8cm

Find the area and perimeter of the circles with following: Radius = 10.5cm

Find the area and perimeter of the circles with following: Diameter = 77cm

Find the area and perimeter of the circles with following: Diameter = 35cm

Find the area and perimeter of the following semicircles: Radius = 1.4cm

Find the area and perimeter of the following semicircles: Diameter = 7cm

Find the area and perimeter of the following semicircles: Diameter = 5.6cm

Find the area of a circular field that has a circumference of 396m.

Find the circumference of a circle whose area is 81πcm².

The diameter of a wheel is 1.4m. How many revolutions does make in moving a distance of 2.2km?

The circumference of a circle exceeds its diameter by 450 cm. Find the area of the circle.

The circumference of a circle is numerically equal to its area. Find the area and circumference of the circle.

The sum of the circumference and diameter of a circle is 176 cm. Find the area of the circle.

Find the radius and area of the circle which has circumference equal to the sum of circumferences of the two circles of radii 3 cm and 4 cm respectively.

The diameter of two circles are 28 cm and 24 cm. Find the circumference of the circle having its area equal to sum of the areas of the two circles.

The radii of two circles are in the ratio 5 : 8. If the difference between their areas is 156p cm², find the area of the bigger circle.

The diameters of three wheels are in the ratio 2 : 4 : 8. If the sum of the circumferences of these circles be 132 cm, find the difference between the areas of the largest and the smallest of these wheels.

The wheel of a car makes 10 revolutions per second. If its diameter is 70cm, find the speed of the car in km per hr.

The speed of a car is 66km per hour. If each wheel of the car is 140cm in diameter, find the number if revolution made by each wheel per minute.

A cart wheel makes 9 revolutions per second. If the diameter of the wheel is 42cm, find its speed in km per hour. (Answer correct to the nearest km)

A bucket is raised from a well by means of a rope wound round a wheel of diameter 35 cm. If the bucket ascends in 2 minutes with a uniform speed of 1.1 m per sec, calculate the number of complete revolutions the wheel makes in raising the bucket.

The circumference o a garden roller is 280cm. How many revolutions does it make in moving 490m?

The diameter of a cycle wheel is `4(5)/(11)"cm"`. How many revolutions will it make in moving 6.3km?

The area of the circular ring enclosed between two concentric circles is 88 cm². Find the radii of the two circles, if their difference is 1 cm.

Find the area enclosed between two concentric circles, If their radii are 6cm and 13cm respectively.

The area between the circumference of two concentric circles is 2464cm². If the inner circle has a circumference of 132cm, calculate the radius of the outer circle.

A wire when bent in the form of a square encloses an area of 484cm². If the same wire is bent into the form of a circle, find the area of the circle.

A wire bent in the form of an equilateral triangle has an area of `121sqrt(3)"cm"^2`. If the same wire is bent into the form of a circle, find the area enclosed by the wire.

Find the circumference of the circle whose area is 25times the area of the circle with radius 7cm.

The circumference of a circle is equal to the perimeter of a square. The area of the square is 484 sq.m. Find the area of the circle.

A wire in the form of a circle of radius 42cm. It is bent into a square. Determine the side of the square and compare the area of the regions enclosed in the two cases.

A 7m wide road surrounds a circular garden whose area is 5544m². Find the area of the road and the cost of tarring it at the rate of Rs.150 per m².

A 4.2m wide road surrounds a circular plot whose circumference is 176m. Find the cost of paving the road at Rs.75per m².

Two circles touch each other externally. The sum of their areas is 58πcm² and the distance between their centres us 10cm. Find the radii of the two circles.

The sum of diameters of two circles is 112cm and the sum of their areas is 5236cm². Find the radii of the two circles.

The sum of the radii of two circles is 10.5 cm and the difference of their circumferences is 13.2 cm. Find the radii of the two circles.

A lawn is in the shape of a semicircle of diameter 42m. the lawn is surrounded by a flower bed of width 7m all round. Find the area of the flower bed in m².

A square is inscribed in a circle of radius 6 cm. Find the area of the square. Give your answer correct to two decimal places if `sqrt(2)` = 1.414.

The cost of fencing a circular field at the rate of Rs.250 per metre is Rs.55000. The field is to be ploughing at the rate of Rs.15 per m². Find the cost of ploughing the field.

Find the area enclosed between two concentric circles of radii 6.3cm and 8.4cm. A third concentric circle is drawn outside the 8.4cm circle. So that the area enclosed between it and the 8.4cm circle is the same as that between the two inner circles. Find the radii of the third circle correct to two decimal places.

Find the area of the biggest circle that can be cut from a rectangular piece 44cm by 28cm. also, find the area of the paper left after cutting out the circle.