Question

please help me in this question no; 2 please

Answer 1

$\sf\large\underline{Given:}$

• $\sf{The\: parallel\: sides=25m\:and\:10m}$
• $\sf{The\:non\:parallel\: sides=14m\:and\:13m}$

$\sf\large\underline{To\: Find:}$

• $\rm{The\: area\:of\: field}$

$\sf\large\underline{Solution:}$

• [At first we have to calculate the ∆ of perpendicular than calculate the area of field]

As we know that,in parallelogram the opposite sides are equal

$\rm{\implies BE=AD=13m}$

$\rm{\implies AB=ED=10m}$

$\rm{\implies EC=CD-ED}$

$\rm{\implies EC=25-10}$

$\rm{\implies EC=15m}$

• Now, find the area of∆ by heron's formula

$\sf{\implies Let\:sides\:of\triangle=a,\:b,\:c}$

$\rm{\implies Here,\:a=14\:\:b=15m\:\:c=13}$

$\sf\large\underline{Formula\:used:}$

$\rm{\implies S=\dfrac{a+b+c}{2}}$

$\rm{\implies Area\:of\triangle=\sqrt{s(s-a)(s-b)(s-c)}}$

• [Now, calculate,semiperimeter here]

$\rm{\implies S=\dfrac{14+15+13}{2}}$

$\rm{\implies S=\dfrac{42}{2}}$

$\rm\green{\implies S=21m}$

• [Than, calculate the area of ∆ here]

$\rm{\implies Area\:of\triangle=\sqrt{s(s-a)(s-b)(s-c)}}$

$\rm{\implies Area\:of\triangle=\sqrt{21(21-14)(21-15)(21-13)}}$

$\rm{\implies Area\:of\triangle=\sqrt{21*7*6*8}}$

$\rm{\implies Area\:of\triangle=\sqrt{7056}}$

$\rm{\implies Area\:of\triangle=84\:m^2}$

• [Now calculate perpendicular of ∆]

$\rm{\implies Area\:of\triangle=\dfrac{1}{2}*base*height}$

• [Here in∆ BEC has height=BF and base=CE]

$\rm{\implies \dfrac{1}{2}*15*BF=84}$

$\rm{\implies 15BF=84*2}$

$\rm{\implies 15BF=168}$

$\rm\green{\implies BF=11.2m}$

Hence,

$\rm\purple{\implies Area_{field}=\dfrac{1}{2}*(sum\:of\: parallel\: sides)*height}$

$\rm{\implies Area\:_{field}=\dfrac{1}{2}*(AB+DC)*BF}$

$\rm{\implies Area\:_{field}=\dfrac{1}{2}*(10+25)*11.2}$

$\rm{\implies Area\:_{field}=\dfrac{1}{2}*35*11.2}$

$\rm\red{\implies Area\:_{field}=196\:m^2}$

Answer 2

Step-by-step explanation:

Solve 1st area of triangle and than arae of field

by solving we get

area of triangle =84m2

now calculate height ∆

84=1/2*15*height

height=11.2m

hence,area of field=1/2×sum of parallel sides×height

Area of field=1/2×35×11.2

Area of field=196m2