Question

PLZ HELP, AND PLZ EXPLAIN

Answer 1

C

Explanation:

To make it easy let's start by organizing our information :

• AC=12 AND BD=8
• ABCD is a rhombus
• K and L are the midpoints of sides AD and CD
• we notice that the rhombus ABCD is divided into four right triangles

What do you think of when you hear a right triangle ?

• The pythagorian theorem !

AC and BD are khown so let's focus on them .

If we concentrated we can notice that AB and BD are cossing each other in the midpoints . why ?

Simply because they are the diagonals of a rhombus .

ow let's apply the pythagorian theorem :

• (AC/2)² + (BD/2)² = BC²
• 6²+4²=52
• BC²= 52⇒
  `√(52)`=BC

Now we khow that : AB=BC=CD=AD=
`√(52)`

This isn't enough . Let's try to figure out a way to calculate the length of KL wich is the base of the triangle

• KL is parallel to AC
• k is the midpoint of AD and L of DC

I smell something . yes! Thales theorem

• KL/AC=DL/DC=DK/AD WE4LL TAKE OLY ONE

• KL/12=
  `√(52)`/2*
  `√(52)`
• KL/12=1/2⇒ KL=6

Now we have the length of the base kl

Now the big boss the height :

• notice that you khow the length of KL
• BD crosses kl from its midpoint and DL =
  `√(52)` /2

What I want to do is to apply the pythgorian thaorem to khow the lenght of that small part that is not a part of the height of the triangle . I will call it D

• DL²=(KL/2)²+D²
• 52/4= 9+ D²
• D² = 52/4-9 +4 SO D=2

now the height of the trigle is H= BD-D= 8-2=6

NOw the area of the triangle is :

• A=(KL*H)/2 ⇒ A= (6*6)/2=18

THE ANSWER IS 18 SQ.UN