Question

Abcd is a parallelogram and x is the midpoint of AB if area of triangle ADC is 24cm square then find area of AXCD?

Answer 1

GIVEN
X is the m.p. of AB
ar.AXCD=24cm^2

TO FIND
the ar.ABC

SO,
ar.AXC=1/2 ar.ABC (CX is the median as X is the m.p.)
ar.ABC=ar.ADC (AC is the diagonal and the diagonal divides the //gm into 2                                      cong.triangles)
Ar.AXCD=1/2 ar.ADC+ADC
AR.AXC=1/3 ADC=8cm^2
hence ar.ABC=8*2=16cm^2

Answer 2

Answer:

The area of AXCD is 36 cm².

Step-by-step explanation:

Given information: ABCD is a parallelogram and x is the midpoint of AB. Area of triangle ADC is 24 cm square.

Here, CD is the diagonal of parallelogram. It means CD divide the area of parallelogram in two equal parts.

$Area(ACD)=Area(ACB)$

$24=Area(ABC)$

X is the midpoint of AB. It means CX is median of ABC.

$Area(ACX)=Area(XBC)$

We know that

$Area(ACX)+Area(XBC)=24$

$2\times Area(ACX)=24$

$Area(ACX)=12$

The area of AXCD is

$Area(AXCB)=Area(ADC)+Area(ACX)$

$Area(AXCB)=24+12=36$

Therefore the area of AXCD is 36 cm².