Tag: Mensuration Exercise 15.6 – class 10

Mensuration Exercise 15.6 – Class 10

Mensuration Exercise 15.6 – Questions

  1. Draw a plan and calculate the area of a level ground using the information given below:
 Metre to C 

To D 120

To E 180

220
210
120
80
 

200 to B

 From A 

 

  1. Plan out and find the area of the field from the date given from the Surveyor’s field book.
 Metre to C 

To D 100
To C 75

To B 50

350
300
250
150
50

150 to F

100 to G

 From A 

 

  1. Sketch a rough plan and calculate the area of the field ABCDEFG from the following data:
 Metre to D 

To E 90

To F 60
To G 15

225
175
125
100
80
60
 

20 to C

70 to B

 From A 

 

  1. Calculate the area of the field shown in the diagram below: {measures in Meters}
  2. Mensuration Exercise 15.6

 

Mensuration Exercise 15.6 – Solutions

  1. Draw a plan and calculate the area of a level ground using the information given below:
 Metre to C 

To D 120

To E 180

220
210
120
80
 

200 to B

 From A 

Solution:

Mensuration Exercise 15.6

Take a scale 20m = 1cm

area of ABCDE = area of ∆APE + trapezium PEDR + area of ∆CDR + area of ∆CQB + area of ∆AQB

= 1/2 bh + 1/2 h(a+b) + 1/2 bh + 1/2 bh + 1/2 bh

= 1/2 x 80 x 180 + 1/2 x 130(180+120) + 1/2 x 10 x 120 + 1/2 x 100 x 200 + 1/2 x 200 x 120

area of ABCDE = 49,300 m2

 

  1. Plan out and find the area of the field from the date given from the Surveyor’s field book.
 Metre to E 

To D 100
To C 75

To B 50

350
300
250
150
50

150 to F

100 to G

 From A 

Solution:

Mensuration Exercise 15.6Scale 20 m = 1 cm

Area of ABCDEFG = area of ∆ABP + area of trapezium PRBC + area of trapezium SRCD + area of ∆DES + area of ∆EFS + area of trapezium SFGQ + area of ∆AQG

= 1/2 bh + 1/2 h(a+b) + 1/2 h(a+b) + 1/2 bh + 1/2 bh + 1/2 h(a+b) + 1/2 bh

= 1/2 x 50 x 50 + 1/2 x 200(50 + 75) + 1/2 x 50(100 + 75) + 1/2 x100 x 50 + 1/2 x 50 x 150 + 1/2 x 150 x (100 + 150) + 1/2 x 100 x 150

= 50,625 m2

 

  1. Sketch a rough plan and calculate the area of the field ABCDEFG from the following data:
 Metre to D 

To E 90

To F 60
To G 15

225
175
125
100
80
60
 

20 to C

70 to B

 From A 

Solution:

Mensuration Exercise 15.6Scale 20 m = 1cm

Area of ABCDEFG = area of ∆AGQ + area of trapezium QRFG + area of trapezium RTEF + area of ∆TED + area of ∆DSC + area of trapezium SCBP + area of ∆APB

= 1/2 bh + 1/2 h(a+b) + 1/2 h(a+b) + 1/2 bh + 1/2 bh + 1/2 h(a+b) + 1/2 bh

= 1/2 x 80 x 15 + 1/2 x20(15+60) + 1/2 x75(60+ 90) + 1/2 x 50 x 90 + 1/2 x 100 x 20 + 1/2 x 65 x(70 + 20) + 1/2 x 60 x 70

= 15250 m2

  1. Calculate the area of the field shown in the diagram below: {measures in Meters}

Mensuration Exercise 15.6

Solution:

Metre To C
40 to C
30 to E
130
95
70
30 to B
From A

Scale 20 m = 1cm

Area of ABCDE = area of ∆AFE + area of trapezium CFEG + area of ∆BCG + area of ∆ABG

= 1/2 bh + 1/2 h(a+b) + 1/2 bh + 1/2 bh

= 1/2 x 95 x 30 + 1/2 x 35(30+40) + 1/2 x 60 x 30 + 1/2 x 70 x 30

= 4,600 m2