Areas of Different Plane Figures

Q.

The cost of levelling a square lawn at Rs 15 per square metre is Rs 19, 935.Find the cost of fencing the lawn at Rs 22 per metre.

Q. Lengths of the diagonals of a rhombus are 15 cm and 24 cm, find its area.

Q. If length of a diagonal of a rhombus is 30 cm and its area is 240 sq cm, find its perimeter.

Q. Lengths of the diagonals of a rhombus are 16.5 cm and 14.2 cm, find its area.

Q. Lengths of diagonals of a rhombus ABCD are 16 cm and 12 cm. Find the side and perimeter of the rhombus.

Q. The cost of fencing a square field at 60 paise per meter is Rs 1200. Find the cost of reaping the field at the rate of 50 paise per 100 sq meters

Q.

Question 57

State whether the following statement is true or false:

The area of a trapezium becomes 4 times if its height gets doubled.

Q. Areas of some circles are given below find their diameters.
(1) 176 sq cm
(2) 394.24 sq cm
(3) 12474 sq cm

Q. The cost of ploughing a square field at 13.50 Rs per sq. is 5400 Rs . Find the cost of fencing the field at 28.50 Rs per metre.

Q. The perimeter of a rhombus is 52 cm. If the diagonal of the rhombus is 10 cm, then the area of the rhombus will be Options: 100 cm2 120 cm2 150 cm2 240 cm2

Q.

How long will a girl take to walk around the boundary of a square field of area $9$ hectars at the rate of $6$ kilometers per hour?

Q.

The cost of levelling a square ground at Rs 1.80 per meter square is 91936.80. Find the cost of fencing at rs 2.25 per meter.

Q.

The area of a square field is 65536m²

^{Find the cost of fencing it at the rate of Rs. 5 per metre}

Q. Area of a trapezium = $\frac{1}{2}\times height\times$ sum of the ___ sides.

1. intersecting
2. parallel
3. adjacent
4. opposite

Q. The sides of a triangle are in ratio 2:3:4. If it's perimeter is 225 units, find the smallest side.

1. 25 units
2. 100 units
3. 50 units
4. 16 units

Q. Perimeter of a regular octagon of side 6 cm is 36 cm.

1. True
2. False

Q. A rhombus is formed by two radii and two chords of a circle whose radius is 16 metres. The area of the rhombus in square metre is:

1. 512
2. $512\sqrt{3}$
3. $128\sqrt{3}$
4. 128
   

Q.

The cost of levelling a square lawn at RS 15 per square meter is rs19935.Find the cost of fencing the lawn at rs 22 per meter

Q. 5. one of the diagonal s of a rhombus of perimeter is 140 M is 60 M find its area and length of the Other diagonal

Q. The area of a square grou d is 6084 sq.m.It is fenced at the rateof Rs 40 per metre and ploughed at the rate of Rs20 per Square metre. Find the total cost.

Q. 31. one of the diagonals of a rhombus of a perimeter 140 metres is 60 metres . find its area and length of the Other diagonal

Q.

If the diagonals of a rhombus get doubled, then the area of the rhombus becomes __________ its original area.

Q. This section contains 1 Assertion-Reason type question, which has 4 choices (a), (b), (c) and (d) out of which ONLY ONE is correct.
इस खण्ड में 1 कथन-कारण प्रकार का प्रश्न है, जिसमें 4 विकल्प (a), (b), (c) तथा (d) दिये गये हैं, जिनमें से केवल एक सही है।

A : If the lengths of diagonals of a rhombus are in the ratio 4 : 3 and its area is 216 cm², then the perimeter of the rhombus is 60 cm.
A : यदि एक समचतुर्भुज के विकर्णों की लम्बाईयाँ 4 : 3 के अनुपात में हैं तथा इसका क्षेत्रफल 216 cm² है, तब समचतुर्भुज का परिमाप 60 cm है।

R : Diagonals of a rhombus are perpendicular to each other.
R : एक समचतुर्भुज के विकर्ण एक दूसरे के लम्बवत् हैं।

1. Both (A) and (R) are true and (R) is the correct explanation of (A)
   
   (A) तथा (R) दोनों सही हैं तथा (R), (A) का सही स्पष्टीकरण है
2. Both (A) and (R) are true but (R) is not the correct explanation of (A)
   
   (A) तथा (R) दोनों सही हैं लेकिन (R), (A) का सही स्पष्टीकरण नहीं है
3. (A) is true but (R) is false
   
   (A) सही है लेकिन (R) गलत है
4. (A) is false but (R) is true
   
   (A) गलत है लेकिन (R) सही है

Q.

A man , after tour , finds that he had spent every day as many rupees as the number of days he had been on tour . How long did his tour last , if he had spent in all Rs. 1296?

Q. A boy walks diagonally across a square lot. What percent does he save by not walking along the edges (approximately)?

1. 22
2. 29
3. 33
4. 20
5. 24

Q. Find the area of a rhombus whose side is $6cm$ and whose altitude is $4cm$. If one of its diagonal is $8cm$ long, find the length of the other diagonal.

Q. (i) Calculate the arc length of a sector whose perimeter and radius are $35$ cm and $8$ cm respectively.
(ii) Find the radius of a sector whose perimeter and arc length are $24$ cm and $7$ cm respectively.

Q. If the area of rhombus is 48 cm sq. and one of its diagonals is 12 cm, find the side of the rhombus.

Q. A rectangular box must hold $60$ cubic decimetres of material. Its length, breadth and height are in the ratio $3:4:5$. We have to paint all the six of its surfaces. If the paint costs $10$ rupees per square metre, then the total cost of painting the box will be:

1. $94$ paise
2. Rs. $1.40$
3. Rs. $9.40$
4. Rs. $19.40$

Q. The cross-section of a canal is in the form of a trapezium. If the canal top is $10m$ wide and the bottom is $6m$ wide, and the area of cross-section is $72m^2$, then the depth of the canal is

1. $10m$
2. $7m$
3. $6m$
4. $9m$