Question

In the figure, the diagonals of a quadrilateral split it into four triangles The areas of three of them are shown in the picture: Calculate the area of the whole quadrilateral. it's only sex for me​

Answer 1

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.)

Learn more :-

in triangle ABC seg DE parallel side BC. If 2 area of triangle ADE = area of quadrilateral DBCE find AB : AD show that B...

https://brainly.in/question/15942930

2) In ∆ABC seg MN || side AC, seg MN divides ∆ABC into two parts of equal area. Determine the value of AM / AB

https://brainly.in/question/37634605