B Nirmala Shastry solutions for मॅथेमॅटिक्स [अंग्रेजी] कक्षा ९ आयसीएसई chapter 17 - Mensuration [Latest edition]

Find the area of triangle with following sides. [All measures are in cm.]

10, 17, 21

Find the area of triangle with following sides. [All measures are in cm.]

17, 25, 28

Find the area of triangle with following sides. [All measures are in cm.]

25, 39, 40

The sides of a triangle are in the ratio 5 : 12 : 13. If its perimeter is 90 cm, find the area of the triangle.

In ΔABC, ∠A = 90°, AB = 14 cm, AC = 48 cm. Find the

1. area of ΔABC 
2. length of perpendicular from A to BC

In ΔPQR, ∠Q = 90° and PQ = QR = 6 cm. Calculate the

1. area of triangle
2. length of perpendicular from Q to PR  [Take `sqrt2 = 1.414`]

Find the area of an isosceles right triangle with hypotenuse 40 cm.

The base of an isosceles triangle is 40 cm and its area is 420 cm². Find the length of its equal sides.

In an isosceles triangle, the unequal side is 22 cm and perimeter is 144 cm. Find its area.

Find the area of an equilateral triangle with side 8 cm. [Take `sqrt3 = 1.732`].

If the area of an equilateral triangle is `25 sqrt(3)  cm^2`, find its perimeter.

In the figure given below, PQR is an equilateral triangle of side 20 cm. ΔQSR is inscribed in it, ∠QSR = 90°, QS = 16 cm. Find (i) SR, (ii) the area of the shaded portion. [Take `sqrt3 = 1.732`].

In ΔABC, AB = 15 cm, AC = 20 cm and ∠BAC = 90°. Find the

1. area of ΔABC
2. length of AD if AD ⊥ BC
3. area of ΔABD

In triangle PQR, ∠Q = ∠R = 45° and QR = 10 cm. Find its area.

The perimeter of an isosceles triangle is 32 cm. The base is 2 cm more than each of the equal sides. Find the area of the triangle.

A triangular advertising board is 13 dm, 14 dm and 15 dm in length. Find the cost of painting it at ₹ 10 per dm².

Find the cost of levelling a triangular piece of land measuring 80 m, 41 m and 41 m, if the rate is ₹ 12 per m².

In ΔABC, AB = 4 cm, altitude CF = 6 cm and AC = 3 cm. Find the length of altitude BE.

In the figure given below, ∠ADB = 90°, AD = 9 cm, BD = 12 cm, BC = 25 cm and AC = 20 cm. Find the (i) length of AB (ii) area of shaded part.

The base of an isosceles triangle is 16 cm. If the height on the base is 4 cm shorter than the equal sides, find the sides, height and area of the triangle.

The base and height of a triangle are in the ratio 7 : 5. If the area of the triangle is 280 cm², find its base and height.

In the given figure ABCDE, EY = CY = 4 cm, AX = BX = 6 cm, DE = DC = 5 cm, DX = 9 cm. DX is perpendicular to EC and AB. Find the area of ABCDE.

Area of parallelogram PQRS is 64 cm² and PR = 10 cm. If ST is perpendicular to PR, find the length of ST.

Find the area of the following trapezium.

Find the area of the following trapezium.

Find the perimeter and area of trapezium PQRS.

In the trapezium ABCD, AD || BC, AB = 25 cm, BC = 76 cm, CD = 39 cm, AD = 20 cm, find its area.

A triangular piece is removed from the rectangle. Find the remaining area.

In trapezium PQRS, PQ = 20 cm, PR = 61 cm, SR = 60 cm and PS ⊥ SR. Find its area.

A rectangle ABCD consists of 5 congruent rectangles as shown in the figure. If the area of the rectangle ABCD is 320 cm², find the dimensions of one small rectangle.

In parallelogram PQRS, PQ = 25 cm, QR = 39 cm and diagonal PR = 56 cm. Find its area.

In the quadrilateral ABCD, AB = 40 cm, BC = 18 cm, CD = 24 cm, AD = 50 cm and ∠C = 90°. Find the (i) length of BD (ii) area of ABCD.

The area of an isosceles trapezium is 80 cm². If the parallel sides are 4 cm and 16 cm, find the (i) height and (ii) length of non-parallel sides.

The diagram represents the cross-sections of a loft PQRST, PTQ is an isosceles triangle and QRST is a rectangle.

The height PN of P above the ground is 7.5 m. The height QR is 5 m and PQ is 6.5 m. Given that N is the mid-point of SR, find the length of SR and the area of PQRST.

Find the area and perimeter of a rhombus whose diagonals measure 18 cm and 24 cm.

ABCD is a rhombus of side 20 cm. If PC = 32 cm, and AP ⊥ CD, find its area.

If the perimeter of a rhombus is 68 cm and one of its diagonals is 30 cm, find its area.

If the area of a rhombus is 864 cm² and one of its diagonals is 48 cm, find the other diagonal and perimeter.

In the quadrilateral ABCD, ∠ACB = 90°, AB = 20 cm, BC = 12 cm and AD = CD = 17 cm. Find (i) AC (ii) area of quadrilateral ABCD.

The perimeter of a quadrant is 50 cm. Find its diameter. `["Take"  π = 22/7]`

Find the area and circumference of a circle with radius 3.5 cm.

ABCD is a square paper of side 14 cm. If a quadrant with B as centre is cut off, find the area of the remaining paper.

OACB is a quadrant of a circle of radius 3.5 cm with centre O. If OD = 2 cm, calculate the area of the shaded region.

Find the shaded area in the given circle with radius 20 cm, ∠AOB = 90°. [Take π = 3.14]

ABCD is a rectangle inscribed in a circle. If AB = 16 cm, BC = 12 cm, find the radius and the area of the shaded part of the circle. [Take π = 3.14].

PQ is the diameter of the semicircle with centre O. OR is the diameter of the small circle inscribed in it. Find the shaded area if PQ = 21 cm.

Calculate the area of the shaded portion. The quadrants shown in the figure are each of radius 7 cm.

The cost of fencing a circular field at the rate of ₹ 24 per metre is ₹ 5280.

Calculate: 

1. the radius of the field. 
2. the cost of ploughing the field at the rate of ₹ 2 per m².

Two small circles touching each other externally and of radius 6 cm are inscribed in a circle. Find the shaded area. [Take π = 3.14]

Two semicircles and one circle of same radius 5 cm are inscribed in a rectangle. Find the area of shaded region. [Take π = 3.14]

Triangle PQR is inscribed in a semicircle. PQ = PR = 7 cm. Find the shaded area.

Triangle ABC is inscribed in a semicircle. AB = 12 cm, BC = 16 cm. Find

1. AC 
2. the shaded area. [Take π = 3.14]

A piece of wire 32 cm long is bent to form the figure given below. APD is a semicircle and AB = BC = CD. Find the radius and area of the figure.

A square is inscribed in a circle. If the area of the shaded region is 224 cm², calculate

1. the radius 
2. area of the square.

Two semicircular flower beds are made on the outside of the smaller sides of a rectangular garden 16 m by 7 rn. Find the total area and perimeter of the garden.

Find the shaded area in the given rectangle: AB = 40 cm, BC = 21 cm.

1. Find the radius of the incircle of ΔABC, AB = 7 cm, BC = 24 cm and ∠B = 90°.
2. Find the shaded area. [Take π = 3.14]

ABCD is a rectangle with AB = 42 cm and BC = 28 cm. Two quadrants with centres D and C are drawn. Find the shaded area.

O is the centre of the circle. OR is the diameter of the smaller circle. RO = 7 cm. Find the area of the shaded region.

In figure, OA = 7 cm, AB = 3.5 cm. Calculate the perimeter and area of the shaded region.

Area of a triangle is 24 cm² and its height is 6 cm. Its base is ______.

Area of a square is 144 cm². Its perimeter is ______.

Perimeter of a square is 140 cm. ∴ Its area is ______.

Two sides of a parallelogram are 8 cm and 6 cm. The distance between the longer sides is 3 cm. The distance between the shorter sides is ______.

The height of a trapezium is 3 cm and its area is 18 cm². If one parallel side is 4 cm, the other parallel side is ______.

The diameter of a circle is 14 cm. Its area is ______.

If the area of a circle is 1386 cm², its radius is ______.

Perimeter of a rectangle is 26 cm, its length is 8 cm. ∴ Its area is ______.

The diagonal of a rectangle is 15 cm and length is 12 cm. ∴ Its area is ______.

The diagonals of a rhombus are 48 cm and 36 cm long. ∴ Its perimeter is ______.

The perimeter of a rhombus is 100 cm. Its one diagonal is 48 cm. Its other diagonal is ______.

The perimeter of a rhombus is 100 cm. Its one diagonal is 48 cm. Its area is ______.

When the radius of a circle is doubled its area ______.

ABCD is a rectangle. AB = 10 cm, BC = 7 cm. The perimeter of the shaded part is ______.

ABCD is a square of side 7 cm. A semicircle is drawn on side AD. The perimeter of the figure is ______.

Area of ABCD is ______.

Perimeter of the figure in cm is ______.

In ΔABC, AB = BC, ∠B = 90°, AC = 10 cm. Area of ΔABC is ______.

The cost of ploughing a field at ₹ 16 per m² is ₹ 2464. ∴ The area of the field is ______.

The radius of a circle whose area is equal to the sum of the areas of 2 circles with radii 6 cm and 8 cm is ______.

The measure of one side of an equilateral Δ is 30 cm. Its area is ______.

Assertion: If the outer and inner diameters of a circular path are 10 m and 4 m, then the area of the path is 21π m².

Reason: Area of a circular path with radii R and r is given by π(R² – r²).

Assertion: In the trapezium ABCD, BC || AD. If AD = 8 cm, BC = 6 cm, CP = `sqrt(120)` cm and AB = 11 cm = CD then AC = 13 cm.

Reason: In a right angled triangle, (base)² + (height)² = (hypotenuse)².

Assertion: If square ABCD and ΔPQR have same perimeter then QR = 8 cm.

Reason: Perimeter = 28 cm, x = 11.

Diameter AB and CD are perpendicular to each other. Radius is 7 cm.

Assertion: The perimeter of the shaded region is πr + 2r.

Reason: The perimeter of a semi-circle is πr + 2r.

Assertion: The diagonals of a rhombus are 6 cm and 8 cm. Its side is 10 cm.

Reason: The diagonals of a rhombus bisect each other at right angles.

Assertion: AB is the diameter of the large semicircle with centre o and radius R. Two smaller semi-circles are drawn on AO and OB. The perimeter of the shaded part is 27πR.

Reason: The perimeter of a semi-circle is πR + 2R.

Find the area of ABCDE where BC = 5 cm, CD = 18 cm, DE = 14 cm and AE = 6 cm.

Find the area of quadrilateral PQRS where ∠Q = ∠S = 90° and PQ = 7 cm, PR = 25 cm and RS = 20 cm.

Find the area of a rhombus with side 4 cm and one of its angles is 120°.

In ΔABC, AB = 6 cm, BC = 8 cm and ∠ABC = 90°. An isosceles ΔACD is described on the base of AC where AD = CD = 13 cm. Find (i) AC and (ii) Area of ABCD.

Find the area of isosceles trapezium ABCD where AB = 10 cm, AD = BC = 20 cm and DC = 42 cm.

The area of parallelogram is 450 m². Its base is twice its altitude. Find the length of its base and altitude.

The area of a trapezium is 40 cm². If the parallel sides measure 6 cm and 10 cm, find its height.

In the parallelogram ABCD, AP ⊥ BC and AQ ⊥ CD. Find its area and AQ if AP = 4 cm, AB = 6 cm and AD = 18 cm.

In the given figure, ABCD is a rectangle with AB = 14 cm, BC = 7 cm. If a quarter circle BCEF and semicircle DEG are removed, calculate the area of the remaining part of the rectangle (shaded region). `["Take"  π = 22/7]`

The figure shows a running track around a grassed enclosure which consists of rectangle PQRS with a surrounding semicircular region at each end. PQ = 200 m, PS = 70 m. Calculate

1. the area of the grassed enclosure in m².
2. the outer perimeter of the track if the width of the track is 7 m. `["Take"  π = 22/7]`

A circle is inscribed in ΔABC, AB = AC = 15 cm, BC = 24 cm. Calculate

1. the radius of incircle 
2. the area of the shaded region. [Take π = 3.14]

With centre O, quadrants of 2 circles are drawn. If OA = 5 cm, AB = 7 cm, find the area of the shaded region. `["Take"  π = 22/7]`

The area between two concentric circles is 1078 cm². The circumference of the inner circle is 132 cm. Find the width of the ring.

In ΔABC, AB = BC, AC = 42 cm and ∠B = 90°. On AC as diameter, a semicircle is described. Find the area of the figure.

Calculate the area of the shaded region, if the diameter of the semicircle is 14 cm. `["Take"  π = 22/7]`

The gate at the entrance of a garden looks like the given figure from the front. The length and breadth of each rectangle are 4 m and 70 cm respectively. The width of the entrance is 2.8 m. The top arch is made up of two concentric semicircles. Find

1. the height of the entrance 
2. the area of the face of the gate

In the kite shown alongside, ABCD is a square. BCD is a quadrant of a circle of radius 14 cm and CEF is an isosceles right-angled triangle with CE = CF = 3 cm. Find the area of the shaded portion.

The difference of radii of two circles is 3 cm and the sum of their circumferences is 44 cm. Calculate the radii of the circles.

The area of a circle is equal to the sum of the areas of 3 circles of radii 2 cm, 3 cm and 6 cm. Find the radius and the circumference of the new circle formed.

ABCD is a square with diagonal AC = 56 cm. A circle and two quadrants of same radius are inscribed in it as shown in the figure. Find the shaded area.

A sheet is 11 cm long and 2 cm wide. Circular pieces 0.5 cm in diameter are cut from it to prepare discs. Calculate the number of discs that can be prepared.

In ΔABE, C and D are points on EB. ∠B = 90°, BC = 5 cm, CD = 4 cm and DE = 26 cm. Area of ΔADC = 24 cm². Find the length of x, y and z.