Question

4. Find the perimeter and area of quadrilateral ABCD in which
AB - 9 cm, AD = 12 cm, BD - 15 cm,
CD - 17 cm and ZCBD = 90°
224 42 1078​

Answer 1

Answer: 17*17=15*15+bc*bc

289=225+bc*bc

64=bc*bc

8=bc

perimeter=17+12+9+8

perimeter=46cm

area1 =1/2*8*17=68cm2

area 2=1/2*12*9=54cm2

total area =122cm2

Answer 2

Consider Δ ABD

Using the Pythagoras theorem

AD

2

=AB

2

+BD

2

By substituting the values

17

2

=AB

2

+15

2

On further calculation

AB

2

=64

By taking out the square root

AB=

64

So we get

AB=8cm

We know that

Perimeter of quadrilateral ABCD=AB+BC+CD+AD

By substitution the values

Perimeter = 8+12+9+17

By addition

Perimeter=46cm

We know that area of ΔABD=

2

1

×b×h

It can be written as

Area of ΔABD=

2

1

×AB×BD

By substituting the values

Area of Δ ABC=

2

1

×8×15

On further calculation

Area of ΔABD=60cm

2

Consider ΔBCD

We know that BC=12cm,CD=9cm and BD=15cm

It can be written as a=12cm, b=9cm and c=15cm

So we get

s=

2

a+b+c

s=

2

12+9+15

By division

s=18cm

We know that

Area=

s(s−a)(s−b)(s−c)

By substituting the values

Area=

18(18−12)(18−9)(18−15

So we get

Area=

18×6×9×3

It can be written as

Area=

6×3×6×9×3

On further calculation

Area=6×3×3

By multiplication

Area=54cm

2

So the area of the shaded region=Area of ΔABD+ Area of ΔBCD

By substituting the values

Area of the quadrilateral ABCD=60+54=114cm

2

Therefore, the perimeter is 46cm and the area is 114cm