Question

kalyan has a qudrilateral shaped field. if one of the diagonal of this farm is 220 m and length of prependiculars from the both the edges is 80 m and 130 m, then find the area of of the field.​

Answer 1

AnswEr :

Refer to the Attachment For Image :

we can solve this Question by two Different Methods, I'll Show You How to Solve :

⋆ Method of Solving I :

$\bold{Given} \begin{cases}\sf{Diagonal(PR)=220 \: m} \\ \sf{Perpendicular_1(SM) = 130 \: m} \\ \sf{Perpendicular_2(QN) = 80 \: m} \\ \sf{Area \: of\: Field = ?}\end{cases}$

• Formula for finding Area is :

⇒ Area = $\sf\dfrac{1}{2}$ × Diagonal × Sum of perpendiculars on the diagonal from opposite vertices

⇒ Area = $\sf\dfrac{1}{2}$ × PR × (SM + QN)

⇒ Area = $\sf\dfrac{1}{\cancel2}\times\cancel{220}\times(130 + 80)$

⇒ Area = 110 m × 210 m

⇒ Area = 23,100 m²

⠀

∴ Area of Quadrilateral Field is 23,100 m².

━━━━━━━━━━━━━━━━━━━━━━━━

⋆ Method of Solving II :

we are noticing that this quadrilateral is formed by two Right Angle Triangle one triangle PQR and another one PSR.

For the Area of Quadrilateral we will find Triangle'a Area and Add them :

⇒ Area of Quadrilateral

⇒ Area of ∆PQR + Area of ∆PSR

⇒ ($\sf\dfrac{1}{2}$ × PR × QN) + ($\sf\dfrac{1}{2}$ × PR × SM)

⇒ ($\sf\dfrac{1}{2}$ × 220 × 80) + ($\sf\dfrac{1}{2}$ × 220 × 130)

⇒ (220 × 40) + (220 × 65)

⇒ 220 × (40 + 65)

⇒ 220 × 105

⇒ 23,100 m²

⠀

∴ Area of Quadrilateral Field is 23,100 m².

Answer 2

Refer to image First For all values to understand ..

Given :-----

• ABCD is a Quadrilateral
• Diagonal BD = 220m
• Perpendicular AE = 130m
• Perpendicular CF = 80m

Question :------ we have to Find Area of ABCD.

Formula Used :--

• Area of ∆ = 1/2 × Base × Perpendicular
• Area of Quadrilateral = 1/2 ×( sum of perpendicular)× Base Diagonal

$\textbf{we can solve it by 2 methods..}$

$\textbf{Lets see basic method First .}$

_______________________________________

$\pink{\bold{\underline{\underline{Solution(1)}}}}$

we know that Area of ∆ = 1/2 × Base × perpendicular distance ...

so, Area oF ∆ADC = 1/2 × DB × AE

Area[∆ADC] = 1/2 × 130 × 220 = 14300m²

Similarly,

Area[∆DBC] = 1/2 × 80 × 220 = 8800m²

so,

Area[ABCD] = Area[∆ADC] + Area[∆DBC]

Area[ABCD] = 14300 + 8800 = 23100m² (Ans)

______________________________

$\red{\bold{\underline{\underline{</strong><strong>Solution</strong><strong>(</strong><strong>2</strong><strong>)</strong><strong>}}}}$

$\textbf{Lets solve it by direct Formula now:--}$

Area of Quadrilateral ABCD = 1/2 ×( sum of perpendicular)× Base Diagonal

Area[ ABCD ] = 1/2 × (130+80) × 220

Area[ ABCD ] = 110 × 210

Area[ ABCD ] = 23100m² (Ans)

______________________________

(Hope it Helps you)