# Chapter 24 : Perimeter and Area - Frank Solutions for Class 9 Maths ICSE

Mathematics in ICSE Class 9 is one of the most challenging and trickiest subjects of all. It includes complex topics such as logarithms, expansions, indices and Pythagoras Theorem which are difficult to understand for an average student. TopperLearning provides study materials for ICSE Class 9 Mathematics to make the subject easy and help students to clear all their concepts. Our study materials comprise numerous video lessons, question banks, revision notes and sample papers which help achieve success in the examination.

## Chapter 24 - Perimeter and Area Excercise Ex. 24.1

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 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 cm^{2}. 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.

## Chapter 24 - Perimeter and Area Excercise Ex. 24.2

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

The
area of a square is 36 cm^{2}. How long are its sides?

The
sides of a rectangle are 5 cm and 3 cm respectively. Find its area in mm^{2}.

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 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:

a. area of the parallelogram.

b. distance between its shorter sides

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.

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

The
area of a rhombus is 234 cm^{2}. If its one
diagonal is 18 cm, find the lengths of its side and the other diagonal. Also,
find perimeter of the rhombus.

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
footpath of uniform width runs all around the inside of a rectangular garden
of 40 m x 30 m. If the path occupies 136 m^{2}, find the width of the
path.

How
many tiles, each of area 625 cm^{2}, will be needed to pave a
footpath which is 1 m wide and surrounds a grass plot of size 38 m x 14 m?

A
wire when bent in the form of a square encloses an area of 16 cm^{2}.
Find the area enclosed by it when the same wire is bent in the form of

a. a rectangle whose sides are in the ratio of 1 : 3.

b. an equilateral triangle

## Chapter 24 - Perimeter and Area Excercise Ex. 24.3

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
cm^{2}, 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
area of the circular ring enclosed between two concentric circles is 88 cm^{2}.
Find the radii of the two circles, if their difference is 1 cm.

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 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= 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 m^{2}.
Find the cost of ploughing the field.

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