Question

what is the relation between the area of qutrilataral ABCD of a qutrilataral of triangle in class 8​

Answer 1

Answer:

Here, we will divide the quadrilateral in two triangles (using either of the diagonals), calculate the (positive value of) the areas of each triangle, and add these values to obtain the total area. In the following figure, quadrilateral ABCD has been divided into ΔABD and ΔADC.

Two triangles make a quadrilateral

Now, we separately calculate the areas of the two triangles.

Area of Triangle ABC:

= (1/2) |−3 × (4 − 2) + (−1) × (2 − 1) + 3 × (1 − 4)| = (1/2) |−6 −1 −9| = (1/2) × 16 = 8sq.units

Area of Triangle ACD:

= (1/2) |−3 × (−2 − 2) + 1 × (2 − 1) + 3 × (1−(−2))|

= (1/2)|12 + 1 + 9| = (1/2) × 22 = 11sq.units

Area of Quadrilateral ABCD:

Area(ABCD) = Area(ΔABC) + Area(ΔADC) = 8 + 11 = 19 sq.units

Answer 2

Answer in the attachment

Hope this answer is helpful for you dear :)