In the diagram below, each side of convex quadrilateral $ABCD$ is trisected. (For example, $AP = PQ = QB.$) The area of convex quadrilateral $ABCD$ is $180.$ Find the area of the shaded region.

Akhain1 Mar 28, 2024

#1**+2 **

Note: I will use [] to denote area.

[ABCD] = AD * DC

[ADU] = [BCT] = AD*DU/2 = (AD*DC/3)/2=AD*DC/6

[ADU]+[BCT]=AD*DC/3

[ABTU] = [ABCD]-([ADU]+[BCT]) = 2/3*(AD*DC) = __120__.

hairyberry Mar 29, 2024

#1**+2 **

Best Answer

Note: I will use [] to denote area.

[ABCD] = AD * DC

[ADU] = [BCT] = AD*DU/2 = (AD*DC/3)/2=AD*DC/6

[ADU]+[BCT]=AD*DC/3

[ABTU] = [ABCD]-([ADU]+[BCT]) = 2/3*(AD*DC) = __120__.

hairyberry Mar 29, 2024