Question

4. A field is in the shape of a trapezium whose parallel
sides are 25 m and 10 m. The non-parallel sides
are 14 m and 13 m. Find the area of the field.​

Answer 1

Refer the given pic for the figure.

Construction:

Draw BE∥AD , Draw BM⊥DC 

□ABED is parallelogram where:

AD = BE = 13 m

AB = DE = 10 m

BC = 14 m

=> DC = DE + EC   .as D−E−C

∴EC = 25 − 10

∴EC = 15 m

Now, Using heron's formula,

In ΔBEC,

2s = 13+14+15

s = 21 m

Area of ∆BEC:

A = √[s (s−a)(s−b)(s−c)]

= √[21(21−13)(21−14)(21−15)]

=21 × 8 × 7 × 6

=84 m²

Area of ΔBEC = 84m²

Area of ∆ BCE = 1/2 × BM × EC

BM = 84 × 2/15

BM = 11.2 metres

Now, Area of □ABED = 11.2 × 10

= 112 m²

Area of □ABCD = Area of ∆BEC + Area of □ABED

= 84 + 112

= 196 m²

Area of field = 196 m².

Area of field = 196 m². _____________________________

Answer 2

$\huge\bold{Question :-}$

A field is in the shape of a trapezium whose parallel sides are 25 m and 10 m. The non-parallel sides are 14 m and 13 m. Find the area of the field.

$\huge\bold{Answer :-}$

Construction:

Draw BE ∥ AD , Draw BM⊥DC 

□ABED is parallelogram where:

AD = BE = 13 m

AB = DE = 10 m

BC = 14 m

=> DC = DE + EC   .as D−E−C

∴EC = 25 − 10

∴EC = 15 m

Now, Using heron's formula,

In ΔBEC,

2s = 13+14+15

s = 21 m

Area of ∆BEC:

A = √[s (s−a)(s−b)(s−c)]

= √[21(21−13)(21−14)(21−15)]

=21 × 8 × 7 × 6

=84 m²

Area of ΔBEC = 84m²

Area of ∆ BCE = 1/2 × BM × EC

BM = 84 × 2/15

BM = 11.2 metres

Now, Area of □ABED = 11.2 × 10

= 112 m²

Area of □ABCD = Area of ∆BEC + Area of □ABED

= 84 + 112

= 196 m²

Final Answer :

Area of field = 196 m².

Additional Information :

Heron's formula :-

Ar(Δ) = √[s(s−a)(s−b)(s−c)]

$\sf \red {Hope\:It\:Helps\:!!}$