Measuring Space Perimeter and Area Class 9 Worksheet with Answers Maths Chapter 6

Teachers can assign these Ganita Manjari Class 9 Worksheet and NCERT Class 9 Maths Chapter 6 Measuring Space Perimeter and Area Worksheet with Answers Pdf for daily practice.

Measuring Space Perimeter and Area Worksheet Class 9

Class 9 Maths Measuring Space Perimeter and Area Worksheet

Worksheet On Measuring Space Perimeter and Area Class 9

Multiple Choice Questions

Question 1.
II three sides of a triangle are 6 cm, 8 cm and 10 cm, then altitude of the triangle using the largest side as base will be
(a) 8 cm
(b) 6 cm
(c) 4.8 cm
(d) 4.4 cm
Answer:
(c) 4.8cm

Question 2.
In the given figure, AB – 8 cm. DC – BC = 13 cm and AB || DC. The perimeter of ∆BMC is

(a) 12 cm
(b) 25 cm
(c) 30 cm
(d) 28 cm
Answer:
(c) 30 cm

Question 3.
The radius of a circle is 21 cm, and the central angle of the sector is l2O°. What Is the perimeter of the sector?
(a) 82 cm
(b) 84 cm
(c) 88 cm
(d) 86 cm
Answer:
(d) 86 cm

Question 4.
The circumference of a circle whose area is equal to the sum of the areas of three circles with radii 2 cm, 3 cm, and 6 cm is
(a) 11 cm
(b) 22 cm
(c) 44 cm
(d) 88 cm
Answer:
(c) 44 cm

Question 5.
The boundary of the shaded region consists of semi-circular arcs. The perimeter of the shaded region Is

(a) 44 cm
(b) 66 cm
(c) 88 cm
(d) 132 cm
Answer:
(c) 88 cm

Question 6.
In the adjoining figure, OABC is a square of side 7 cm. OAC is a quadrant of a circle with centre O. The area of the shaded region is

(a) 38,5 cm²
(b) 10.5 cm²
(c) 11.5 cm²
(d) 49 cm²
Answer:
(b) 10.5 cm²

Question 7.
How many times will a wheel of diameter 105 cm revolve to cover a distance of 660 metres?
(a) 2000
(b) 400
(c) 200
(d) 100
Answer:
(c) 200

Question 8.
In the figure, a unit square ROSI’ is inscribed in a circular sector with centre O. Along with the above information, which of these Is SUFFICIENT to find the area of sector POQ?

(a) Area of the square ROST
(b) Radius of sector POQ
(c) Arc length PQ
(d) The given information is sufficient
Answer:
(c) Arc length PQ

Question 9.
In the circle shown below, O is the centre. MN is a chord which subtends an angle of 9O st the centre. The area of the shaded region is 72 cm².What is the radius of the circle?

(a) 6,√7 cm
(b) 6√28 cm
(c) 84 cm
(d) 252 cm
Answer:
(a) 6,√7 cm

Question 10.
Savita has a lamp placed at the centre of her square yard of side measuring 20 m. The light from the lamp covers a circular region of radius 10 m in the yard. What is the area of the yard that is NOT lit by the lamp?
(a) 400 π sq.m
(b) 100 π sq.m
(c) (40 – 10 π) sq. m
(d) (400 — 100 π) sq. m
Answer:
(d) (400 — 100 π) sq. m

Question 11.
In the given figure, 0 is the centre of the circle. PR and RQ are chords of the circle. The radius of the circle is 5 cm. PR = 8cm, QR = 6cm and ∠PRQ = 900. What is the area of the shaded region?

Answer:
(a) \(\left(\frac{25}{4} \pi-24\right) \mathrm{cm}^2\)
(b) \(\left(\frac{25}{2} \pi-24\right) \mathrm{cm}^2\)
(c) \(\left(\frac{25}{4} \pi\right) \mathrm{cm}^2 \)
(d) \(\left(\frac{25}{2} \pi\right) \mathrm{cm}^2 \)
Answer:
(b) \(\left(\frac{25}{2} \pi-24\right) \mathrm{cm}^2\)

Question 12.
The sum of diameters of two circles is 35 cm and the difference of their circumference is 22 cm. The area of the smaller circle will be
(a) 121 cm²
(b) 144 cm²
(c) 154 cm²
(d) 308 cm²
Answer:
(c) 154 cm²

Question 13.
The area of a rhombus whose perimeter is 200 m and one of the diagonal is 80 m is
(a) 2000 m²
(b) 2200 m²
(c) 2400 m²
(d) 2100 m²
Answer:
(c) 2400 m²

Question 14.
The area of a quadrilateral ABCD whose sides are AB = 13 cm, BC = 12 cm, CD = 9 cm, DA = 14 cm and diagonal BD = 15 cm is
(a) 162 cm²
(b) 165 cm²
(c) 138 cm²
(d) 164 cm²
Answer:
(c) 138 cm²

Question 15.
The area of an isosceles triangle each of whose equal sides are 13 cm and base is 24 cm is
(a) 110 cm²
(b) 60 cm²
(c) 130 cm²
(d) 105 cm²
Answer:
(b) 60 cm²

Assertion-Reason

In Q. 1 to 5, two statements are given, one labelled as Assertion (A) and the other labelled as Reason (R). Select the correct answer from the options (a), (b), (c), and (d) given below.
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
(b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
(c) Assertion (A) is true, but Reason (R) is false.
(d) Assertion (A) is false, but Reason (R) is true.

1. Assertion (A): A sector is cut from a circle of radius 42 cm. The central angle of the sector is 120°. The perimeter of the sector is 172 cm.
Reason (R): Perimeter of sector = 2 (radius) + Length of corresponding arc of sector.
Answer:
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).

2. Assertion (A): If the perimeter of a sector of a circle of radius 5.6 cm is 25 cm, then the area of the sector is 38.64 cm².
Reason (R): The area of a sector of a circle of radius (r) with central angle θ is \(\frac{\theta}{360^{\circ}}\) – × πr.
Answer:
(c) Assertion (A) is true, but Reason (R) is false.

3. Assertion (A): The sides of a triangle are in the ratio of 13 : 14 : 15 and its perimeter is 84 m. Then the greatest side is 30 cm.
Reason (R): Perimeter of a triangle = a + b + c, where a, b, c are sides of a triangle.
Answer:
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).

4. Assertion (A): The sides of a triangle are 120 cm, 160 cm and 200 cm. Its area is 9600 cm².
Reason (R): If 2s = (a + b + c), where a, b, c are the sides of a triangle, then area = \(\sqrt{(s-a)(s-b)(s-c)}\)
Answer:
(c) Assertion (A) is true, but Reason (R) is false.

5. Assertion (A): Semi perimeter of an equilateral triangle is s = \(\frac{3 a}{2}\) where a is the side of the triangle.
Reason (R): If the area of an equilateral triangle is 16√3 cm², then the semi perimeter of triangle is 10 cm.
Answer:
(c) Assertion (A) is true, but Reason (R) is false.

Measuring Space Perimeter and Area Class 9 Ganita Manjari Worksheet

Short Answer Type Questions – I

Question 1.
The unequal side of an isosceles triangle is 6 cm and its perimeter is 24 cm. Find its area.
Answer:
18√2 cm²

Question 2.
Sides of a triangle are in the ratio of 12 : 17 : 25 and its perimeter is 540 cm. Find its area.
Answer:
9000 cm²

Question 3.
The length and the breadth of a rectangle are 6 cm and 4 cm respectively. Find the height of a triangle whose base is 6 cm and area is 3 times that of the rectangle.
Answer:
24 cm

Question 4.
Two adjacent sides of a parallelogram are 15 cm and 10 cm. If the distance between 15 cm sides is 8 cm; find the distance between 10 cm sides.
Answer:
12 cm

Question 5.
A ring shaped garden has an inner diameter of 20 m and an outer diameter of 30 m. Find the area of the garden.
Answer:
392.85m²

Question 6.
The radius of a circle is 5 m. Find the circumference of the circle whose area is 49 times the area of the given circle.
Answer:
220 m

Short Answer Type Questions – II

Question 1.
The sides of a triangular field are 1200 m, 1600 m and 2000 m. It is rent out at ₹ 5000 per hectare. Find the rent.
Answer:
₹ 480000

Question 2.
A field in the form of parallelogram has sides of 60 m and 40 m, and one of its diagonals is 80 m long. Find the area of parallelogram.
Answer:
2323.79 m²

Question 3.
Four lamps are fixed on the boundary of a circular garden and joined to form a cyclic quadrilateral. The lengths of the wires joining consecutive lamps are 5 m, 9 m, 10 m and 12 m. Find the area enclosed by . the wires.
Answer:
74.94 m²

Question 4.
The area of a square is the same as that of a rectangle. The length and the breadth of the rectangle are respectively 5 cm more and 4 cm less than the side of the square. Find the side of the square.
Answer:
20 cm

Question 5.
A room is 10 m long, 6 m wide, and 3 m high. It has one door measuring 2 m × 1.5 m and two windows, each measuring 1.5 m × l m. The rate of painting is ?150 per square metre. Find the total cost to paint the walls (excluding the doors and windows).
Answer:
₹13500

Question 6.
In the given figure, AB is a diameter of the circle with centre O and OA = 7 cm. Find the area of the shaded region.

Answer:
66.5 cm²

Question 7.
Four equal circles, each of radius 5 cm, touch one another as shown in the given figure. Find the area of the shaded region enclosed between the circles.

Answer:
21.43 cm²

Long Answer Type Questions

Question 1.
In the given figure, AB = 36 cm and M is the midpoint of AB. Three semicircles are drawn on AB, AM and MB as diameters. A circle with centre C touches all the three circles. Find the area of the shaded region in terms of n.

Answer:
45 π

Question 2.
A floral design on a floor is made up of 16 triangular tiles. The sides of each triangle are 9 cm, 28 cm and 35 cm (See fig.). Find the cost of polishing the tiles at the rate of 50p per cm².

Answer:
₹ 705.60

Question 3.
The sides of a triangular field are in the ratio 4 : 7 : 9. If its perimeter is 400 m, find the area of the field.
Answer:
Area = 5366.56 m²

Question 4.
A bed of roses is shaped as shown in the figure. In the centre, there is a square, and on each side of the square, there is a semicircle. The side of the square is 21 metres. If each rose plant requires 6 m2 of space, find the number of plants that can be planted.

Answer:
189 plants

Case Based Questions

Question 1.
During the annual day function of a school, the organisers decided to give a cash prize along with a memento to their best students. Each memento is shaped as shown in the figure and its base ABCD is shown from the front side. The rate of silver plating is ₹20 per cm².

Based on the above information, answer the following questions:
(a) What is the area of the quadrant ODCO?
Answer:
38.5 cm².

(b) Find the area of AAOB.
Answer:
50 cm²

(c) What is the total cost of silver plating the shaded part ABCD?
Answer:
₹230

OR
What is the length of arc CD?
11 cm

Competency Based Questions

Question 1.
A design is made on a rectangular tile of dimensions 60 cm × 70 cm, as shown in the figure. The design consists of 8 triangles, each of sides 26 cm, 17 cm and 25 cm. Find the total area of the design and the remaining area of the tile.

Question 2.
How much paper of each shade is needed to make the kite given in thefigure, in which ABCD is a square with diagonal 44 cm?

Question 3.
The floor of a room is of dimensions 5 m × 4 m and it is covered with circular tiles of diameter 50 cm each as shown in the figure. Find the area of floor that remains uncovered by the tiles. (Use it = 3.14)

Question 4.
An archery target has three regions formed by three concentric circles, as shown in the figure. If the diameters of the concentric circles are in the ratio 1 : 2 : 3, find the ratio of the areas of three regions.

Question 5.
From two adjacent comers of a square of side 8 cm, quadrants of circles of radius 1.4 cm are cut. Another circle of radius 2.4 cm is also cut from the centre, as shown in the figure. Find the area of the remaining portion of the square.

Activity

Question 1.
Draw an isosceles trapezium on an A4 sheet with suitable dimensions. Divide the trapezium into a parallelogram and a triangle. Measure the sides of these shapes and note them down. Check if the area of the isosceles trapezium is equal to the sum of the areas of the parallelogram and the triangle. Evaluate the general expression for it.

The post Measuring Space Perimeter and Area Class 9 Worksheet with Answers Maths Chapter 6 appeared first on Learn CBSE.

from Learn CBSE https://ift.tt/vxQ1lNE
via IFTTT