Question

in the figure the diagonals of a Quadrilateral Split it into four traingles the area of three of them are shown in the picture calculated the area of the whole quadrilateral​

Answer 1

Answer:

Step-by-step explanation:

A line from the vertex of a triangle divides the length of the opposite side and the area of triangle in the same ratio.

In ∆ ACD, a line DE is drawn from D to AC.

∴ AE : EC = Area ∆ AED : Area of ∆ CED

AE : EC = 60 : 30 = 2 : 1

In ∆ ACB, a line BE is drawn from B to AC.

∴ AE : EC = Area of ∆ AEB : Area of ∆ CEB

Answer 2

Solution :-

we know that,

• A line from the vertex of a triangle divides the length of the opposite side and the area of triangle in the same ratio . { Because height remains same . }

So, Let diagonals AC and BD of given quadrilateral intersect at O .

Now, as we can see that, In ∆ACD, a line DO is drawn from D to AC .

then,

→ AO : OC = Area of ∆AOD : Area of ∆COD

putting given values,

→ AO : OC = 50 : 25

→ AO : OC = 2 : 1

Now, In ∆ACB, a line BO is drawn from B to AC .

then,

→ AO : OC = Area of ∆AOB : Area of ∆COB

again putting values,

→ 2 : 1 = Area of ∆AOB : 40

→ (2/1) = (Area of ∆AOB/40)

→ Area of ∆AOB = 2 * 40

→ Area of ∆AOB = 80 cm² .

therefore,

→ The area of whole quadrilateral = 50 + 25 + 40 + 80 = 195 cm² (Ans.)

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