Find the perimeter and area of the quadrilateral ABCD in which AB = 42 cm, BC = 21 cm, CD = 29 cm, DA = 34 cm and =90⁰.

Question

Find the perimeter and area of the quadrilateral ABCD in which AB = 42 cm, BC = 21 cm, CD = 29 cm, DA = 34 cm and =90 0 .

Philoid · Accepted Answer

Firstly, let us calculate the perimeter of the given quadrilateral

Perimeter of quadrilateral ABCD = 34 + 29 + 21 + 42 = 126 cm

We know that,

Area of triangle =

Area of triangle BCD =

= 210 cm²

Now, we have to calculate the area of triangle ABD,

For this, we have

a = 42 cm

b = 20 cm

c = 34 cm

Therefore,

s =

=

= 48 cm

We know that,

Area of triangle =

Therefore,

Area of triangle ABD =

=

= 4 × 3 × 2 × 14

= 336 cm²

Hence,

Area of quadrilateral ABCD = Area of triangle ABD + Area of triangle BCD

= 336 + 210

= 546 cm²