Find the perimeter and area of the quadrilateral ABCD in which AB = 17cm, AD = 9cm, CD = 12cm, =90⁰ and AC = 15cm.

Question

Find the perimeter and area of the quadrilateral ABCD in which AB = 17cm, AD = 9cm, CD = 12cm, =90 0 and AC = 15cm.

Philoid · Accepted Answer

By using Pythagoras theorem in right triangle ABC, we get

BC=

=

= 8 cm

Let us first find out the perimeter of the given quadrilateral

Perimeter of quadrilateral ABCD = 17 + 9 + 12 + 8 = 46 cm

We know that,

Area of triangle ABC =

=

= 60 cm²

Now,

For area of triangle ACD, we have

a = 15 cm

b = 12 cm

And,

c = 9 cm

Therefore,

s =

=

= 18 cm

Now,

Area of triangle ACD =

=

= 18 × 3

= 54 cm²

Therefore,

Area of quadrilateral ABCD = Area of triangle ABC + Area of triangle ACD

= 60 + 54

= 114 cm²