Math, asked by zainahan01, 5 hours ago

50TL
B 12 cm
12 cm
22. Find the area and perimeter of figure ABCD where ZB = 90° and ZDAC = 90°.
AB = 6 cm, BC = 8 cm and DA= 24 cm.
24 cm​

Answers

Answered by pratyushpatra467
0

Answer:

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

Step-by-step explanation:

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