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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 m2
- 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
- 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
- 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
Breath Math 