Question

find the area of quadrilateral whose vertices ,taken in order are (-4,-2) (-3,-5)+3,-2) and (2,3) ​

Answer 1

Answer:

hey!

Step-by-step explanation:

given : find the area of quadrilateral whose vertices ,taken in order are (-4,-2) (-3,-5)+3,-2) and (2,3) ​

when we plot the given dimesnions form the question ,  we get a a parellogram...i.e two congruent  triangles

now we need to find the area of two congruent  triangles

let A =( -4 , -2 )

     B = (-3 , -5 )

     C = ( 3 , -2 )

      D = ( 2 , 3 )

now in triangle ABD

area = 1/2 { 2*(-2 + 5 ) - 4( -5 -3 ) -3( 3 + 2 ) }

           1/2 { 2*3  -  4* (-8)  - 3 * 5 )

           1/2{ 6 + 32 - 15}

           23/2

therefore area of triangle ABD = 23/2 unit square ------------1

 

now area of triangle BCD

area = 1/2{ -3( -2 -3 ) + 3( 3 + 5 ) + 2( -5 + 2 ) }

           1/2 { -3*-5 + 3*8 + 2*(-3)}

            1/2 { 15 + 24 - 6 }

            33/2

therefore area of triangle BCD = 33/2 unit square ------------- 2

adding 1 & 2

23/2 + 33/2

( 23 + 33 )/2

56 / 2

28

therefore total area = 28 units. square