Question

In a quadrilateral ABC, the diagonal AC = 18 m and the perpendiculars from B and D to AC are 11 m and 9 m respectively. Calculate the area of the quadrilater​

Answer 1

Answer:

We assume ABCD be the quadrilateral having sides AB, BC, CD, DA and ∠ACB = 90∘.

We take a diagonal AC, where AC divides ABCD into two triangles ΔACB and ΔADC

Since ∆ACB is right angled at C, we have

AC = 15 cm; AB = 17 cm

AB2 = AC2 + BC2

Area of right angled triangle ABC, say A1 is given by

, where,

Base = BC = 8 cm; Height = AC = 15 cm

Area of triangle ADC, say A2 having sides a, b, c and s as semi-perimeter is given by

, where

a = AD = 9 cm; b = DC = 12 cm; c = AC = 15 cm

Area of quadrilateral ABCD, say A

A = Area of ∆ACB + Area of ∆ADC

Perimeter of quadrilateral ABCD, say P