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

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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

⟹ ar(ADC) = 1/2(18)(4.3)⟹ ar(ADC) = 9(4.3)

⟹ ar(ADC) = 38.7 cm²

Similarly

,⟹ ar(ABC) = 1/2(18)(5.6)

⟹ ar(ABC) = 9(5.6)

⟹ ar(ABC) = 50.4 cm²

∴ Area of ABCD = ar(ADC + ABC)

➭ Area of quadrilateral = 38.7 + 50.4 = 89.1 cm²

Answer 2

Answer:

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

⟹ ar(ADC) = 1/2(18)(4.3)⟹ ar(ADC) = 9(4.3)

⟹ ar(ADC) = 38.7 cm²

Similarly

,⟹ ar(ABC) = 1/2(18)(5.6)

⟹ ar(ABC) = 9(5.6)

⟹ ar(ABC) = 50.4 cm²

∴ Area of ABCD = ar(ADC + ABC)

➭ Area of quadrilateral = 38.7 + 50.4 = 89.1 cm²