Question

Find the area of a quadrilateral KLMN in which KL=7m ,LM=6m , MN=12m, NA=15m, and KM=9m


​

Answer 1

Step-by-step explanation:

Consider ABCD is a quadrilateral where,

AB=12,BC=5,CD=6,DA=15 and ∠ABC=90

o

Area of ABCD= Area of ΔABC+Area of ΔACD

In Δ ABC, ∠B=90

o

Apply Pythagoras theorem in ΔABC

Therefore, AC

2

=AB

2

+BC

2

=12

2

+5

2

So, AC=13

Area of ΔABC=

2

1

×AB×BC=

2

1

×12×5=30m

2

In ΔACD, let s be the semiperimeter,

S=

2

6+15+13

=17m

Applying Heron's formula,

Area of ΔACD =

S(S−a)(S−b)(S−c)

=

17(17−13)(17−15)(17−6)

=

17(4)(2)(11)

=2

374

Hence, Area of quadrilateral ABCD=30+2

374

So, option C is correct.

Answer 2

Answer:

a) pair of opposite sides: KL & MN, KN & LM

b) pair of opposite angles: ZK & ZL, ZL & ZN

c) pair of adjacent sides: KN & NM, KL & LM

d) pair of adjacent angles: ZK & ZN, ZL & ZM

$\underline\green{▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬}$

☘ᴍᴀʀᴋ ᴍᴇ ᴀs ʙʀᴀɪɴʟɪsᴛ