Question

the diagonal AC of a quadrilateral ABCD is 6cm and the perpendiculars, BM from the vertex B is 3 cm and DN from D is 5 cm , dropped on the same diagonal. find the area of rhe quadrilateral ABCD.​

Answer 1

Given :- the diagonal AC of a quadrilateral ABCD is 6cm and the perpendiculars, BM from the vertex B is 3 cm and DN from D is 5 cm , dropped on the same diagonal. find the area of the quadrilateral ABCD.

Solution :-

we have,

→ Length of diagonal AC = 6 cm

→ Perpendicular distance BM = 3 cm

→ Perpendicular distance DN = 5 cm

so,

→ Area of quadrilateral ABCD = (1/2)[ sum of Perpendicular distance on diagonal ] * Diagonal length

putting values we get,

→ Area of quadrilateral ABCD = (1/2) * (3 + 5) * 6

→ Area of quadrilateral ABCD = 8 * 3

→ Area of quadrilateral ABCD = 24 cm² (Ans.)

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Answer 2

Given : the diagonal AC of a quadrilateral ABCD is 6cm and the perpendiculars, BM from the vertex B is 3 cm and DN from D is 5 cm , dropped on the same diagonal.

To find :  the area of the quadrilateral ABCD.​

Solution:

area of the quadrilateral ABCD.​  = Area of  ΔABC + Area of  ΔADC

Area of triangle = (1/2) * Base * Height

Area of  ΔABC = (1/2) * AC * BM  = (1/2) * 6 * 3  = 9 cm²

Area of  ΔADC = (1/2) * AC * DN  = (1/2) * 6 * 5 = 15 cm²

Area of the quadrilateral ABCD.​  = 9 + 15  = 24   cm²

Area of the quadrilateral ABCD is 24 cm²

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