Question

Find the area of a quadrilateral whose sides are 85 cm , 143 cm, 165 cm and 85 cm and one of the diagonals is 154 cm​

Answer 1

Answer:

hope it's helpful please mark me As Brailiant

Step-by-step explanation:

Correct option is

C

(6+

24

)cm

2

In quadrilateral ABCD,

AB=3 cm,BC=4 cm,CD=2 cm,DA=5 cm and ∠ABC=90

0

Area of ABCD = Area of ΔABC+ Area of ΔACD

In ΔABC,∠B=90

0

∴ Area of ΔABC =

2

1

×AB×BC=

2

1

×3×4 cm

2

=6cm

2

In ΔABC, applying pythagorous theorem we get,

AC

2

=AB

2

+BC

2

⇒AC

2

=3

2

+4

2

⇒AC

2

=9+16

⇒AC

2

=25

⇒AC=5

∴AC=5 cm

In ΔACD, semi-perimeter s=

2

2+5+5

cm=6 cm

Applying Heron's formula,

Area of Δ ACD =

S(S−a)(S−b)(S−c)

=

6(6−5)(6−5)(6−2)

=

6(1)(1)(4)

=

24

Hence, Area of □ABCD=(6+

24

)cm

2

So, option C is correct.