Mensuration Exercise 15.6 – Class 10

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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

 

2. 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

 

3. 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

 

4. Calculate the area of the field shown in the diagram below: {measures in Meters}
5. 

 

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

 

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 m²

 

3. 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

4. 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