10th mathematics exercise questions with answers

# 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 120To 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 75To B 50 350 300 250 150 50 150 to F100 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 90To 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 – Solutions

1. Draw a plan and calculate the area of a level ground using the information given below:
 Metre to C To D 120To E 180 220 210 120 80 200 to B From A

Solution: 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 75To B 50 350 300 250 150 50 150 to F100 to G From A

Solution: Scale 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 90To F 60 To G 15 225 175 125 100 80 60 20 to C 70 to B From A

Solution: Scale 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} 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