Question

Find the area of a quadrilateral one of whose diagonal is 18 cm long and the length of perpendiculars from the other two vertices are 4.3 cm and 5.6 cm respectively *​

Answer 1

✬ Area = 89.1 cm² ✬

Step-by-step explanation:

Given:

• Diagonal of quadrilateral is 18 cm.
• Perpendiculars drawn on diagonal from vertices are of 4.3 and 5.6 cm.

To Find:

• What is the area of quadrilateral ?

Solution: Let ABCD be a quadrilateral in which

• AC = Diagonal = 18 cm.
• DE = Perpendicular on AC = 4.3 cm.
• BF = Perpendicular on AC = 5.6 cm.

Now, in ∆ADC and ∆ABC

• AC = Base
• DE = Height

• AC = Base
• BF = Height

As we know that

★ Area of ∆ = 1/2(Base)(Height) ★

$\implies{\rm }$ ar(ADC) = 1/2(18)(4.3)

$\implies{\rm }$ ar(ADC) = 9(4.3)

$\implies{\rm }$ ar(ADC) = 38.7 cm²

Similarly,

$\implies{\rm }$ ar(ABC) = 1/2(18)(5.6)

$\implies{\rm }$ ar(ABC) = 9(5.6)

$\implies{\rm }$ ar(ABC) = 50.4 cm²

∴ Area of ABCD = ar(ADC + ABC)

➭ Area of quadrilateral = 38.7 + 50.4 = 89.1 cm²

Answer 2

$\huge\mathcal{\green{\underbrace{\orange{SOLUTION:-}}}}$

GIVEN :-

• The diagonal of a quadrilateral is 18cm .

• The length of the perpendicular from the other two vertices are 4.3cm and 5.6cm respectively .

TO FIND :-

• Area of the quadrilateral .

CALCULATION :-

✍️ See the attachment diagram .

✍️ As shown in the diagram,

$\red\checkmark\:\mathcal{\red{\underline{Area\:of\:the\:quadrilateral\:ABCD\:=\:Area\:of\:\triangle{ABC}\:+\:Area\:of\:\triangle{ADC}\:}}}$

$\bigstar\:\rm{\red{\boxed{\purple{Area\:of\:\triangle{ABC}\:=\:\dfrac{1}{2}\:\times{AC}\:\times{BQ}\:}}}}$

$\bigstar\:\rm{\red{\boxed{\purple{Area\:of\:\triangle{ADC}\:=\:\dfrac{1}{2}\:\times{AC}\:\times{DP}\:}}}}$

✍️ Here,

• AC = 18cm .

• DP = 4.3cm .

• BQ = 5.6cm .

$\rm{\implies\:Area\:of\:\Box{ABCD}\:=\:\dfrac{1}{2}\:\times{AC}\times{BQ}\:+\:\dfrac{1}{2}\:\times{AC}\times{DP}\:}$

$\rm{\implies\:Area\:of\:\Box{ABCD}\:=\:\dfrac{1}{2}\:\times{AC}\:\times\:(BQ\:+\:DP)\:}$

$\rm{\implies\:Area\:of\:\Box{ABCD}\:=\:\dfrac{1}{2}\:\times{18}\:\times\:(4.3\:+\:5.6)\:}$

$\rm{\implies\:Area\:of\:\Box{ABCD}\:=\:9\times{9.9}\:}$

$\rm{\green{\boxed{\orange{\implies\:Area\:of\:\Box{ABCD}\:=\:89.1\:cm^2\:}}}}$

$\therefore$ $<font color=baby>$ The area of the quadrilateral is “89.1cm²” .