**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 120 To E 180 | 220210 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 75 To B 50 | 350300 250 150 50 | 150 to F 100 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 90 To F 60 | 225175 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 120 To E 180 | 220210 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 75 To B 50 | 350300 250 150 50 | 150 to F 100 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 90 To F 60 | 225175 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}