Question

Find the perimeter and area of the quadrilateral abcd in which ab=17 cm, and=9cm,cd=29cm, angle acb=90 degree and ac=15cm.

Answer 1

Given that: AB = 17cm

AD = 9cm

CD = 12cm

AC = 15cm

and ∠ACB = 90°

In right angled triangle ACB,



We have to find the area of quadrilateral ABCD.

Area of Quadrilateral ABCD = Area of ΔACB + Area of ΔACD ....... (1)

Now, Area of right angled triangle ACB



We will calculate the area of triangle ACD using Heron's Formula as :



Where a, b, c are the sides of triangle and S is the semi-perimeter of the triangle and is given by



Here, a = 15cm, b = 12cm, c = 9cm.





∴ From (1),

Area of quadrilateral ABCD = (60 + 54) cm2

=114 cm2