the adjoining figure shows a field with the measurements given in metres calculate the area of the field
Answers
Area of quadrilateral ABCDE is 1615 square metre.
Concept:
Area of the trapezium,
A = (a+b)h/2
where a and b are the parallel sides and h is the distance between the parallel lines.
Area of the triangle,
A = (1/2) bh
where h is the height and b is the base of the triangle respectively.
Given:
A figure of a field is given.
Find:
The area of the field given.
Solution:
The area of the given field can be calculated as,
Area of the field, A = ΔABF + ΔDGC + ΔADE + Area of trapezium (BCGH)
Area of the triangle ΔABH,
ΔABH = (1/2)(8)(35) = 140 m²
Similarly,
Area of the triangle ΔDGC,
ΔDGC = (1/2)(14)(40) = 280 m²
Similarly,
Area of the triangle ΔADE,
ΔADE = (1/2)(14+18+8)(26) = 520 m²
Area of the trapezium,
A = (a+b)h/2
A = (40+35)(18)/2 = 675 m²
Total area of the field = (140+280+520+675) m² = 1615 m²
Hence, the area of the field is 1615 m².
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