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Mensuration Exercise 15.6 – Questions
- 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 |
- 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 |
- 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 |
- Calculate the area of the field shown in the diagram below: {measures in Meters}
Mensuration Exercise 15.6 – Solutions
- 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 m^{2}
- 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 m^{2}
- 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 m^{2}
- 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 m^{2}