Question

A field in the shape of a trapezium whose parallel side are 25m and 10m THe non parallel sides are 14m and 13m Find the area of the field

Answer 1

given: ab=10m, cd=25m, ad=13m, bc=14m
construction : draw BE=13m
height of triangle = BF
base of triangle = 15m
solution:
in tri.BEC: semi perimeter,s = a+b+c÷2
=13+14+15÷2=42÷2=21
$area \: of \: tri. = \sqrt{s(s - a)(s - b) (s - c)} \\ = \: \sqrt{21(21 - 13)(21 - 14)(21 - 15) } \\ = \: \sqrt{21 \times 8 \times 7 \times 6 } \\ = \: 7 \times 3 \times 2 \times 2 \\ = 84 {m}^{2}$
now we know that,
area of tri.= 1/2 × base × height
84 = 1/2 × bf × ce
84 = 1/2 × 15 × bf
bf = 84 ×2/15
bf = 11.2 m
area of trapezium abcd = 1/2 × (sum of parallel side) × height
= 1/2 × ( ab+cd) × bf
= 1/2 × (25+10) × 11.2
=1/2 × 35× 11.2
= 196m2