Find the area of quadrilateral ABCD. [Hint: the diagonal divides the quadrilateral into two triangles.]A. 26.47 units²B. 28.53 units²C. 33.08 units²D. 27.28 units²

Answer:Option B [tex]28.53\ units^{2}[/tex]Step-by-step explanation:The area of quadrilateral ABCD is equal to the area of triangle ABD plus the area of triangle ADCwe know thatHeron's Formula is a method for calculating the area of a triangle when you know the lengths of all three sides.  Let  a,b,c be the lengths of the sides of a triangle.  The area is given by:[tex]A=\sqrt{p(p-a)(p-b)(p-c)}[/tex]wherep is half the perimeter[tex]p=\frac{a+b+c}{2}[/tex]step 1Find the area of triangle ABDwe have[tex]a=AB=2.89\ units[/tex][tex]b=BD=8.59\ units[/tex][tex]c=DA=8.6\ units[/tex]Find the half perimeter p[tex]p=\frac{2.89+8.59+8.6}{2}=10.04\ units[/tex]Find the area[tex]A=\sqrt{10.04(10.04-2.89)(10.04-8.59)(10.04-8.6)}[/tex][tex]A=\sqrt{10.04(7.15)(1.45)(1.44)}[/tex][tex]A=\sqrt{149.89}[/tex][tex]A=12.24\ units^{2}[/tex]step 2Find the area of triangle ADCwe have[tex]a=AC=4.3\ units[/tex][tex]b=AD=8.6\ units[/tex][tex]c=DC=7.58\ units[/tex]Find the half perimeter p[tex]p=\frac{4.3+8.6+7.58}{2}=10.24\ units[/tex]Find the area[tex]A=\sqrt{10.24(10.24-4.3)(10.24-8.6)(10.24-7.58)}[/tex][tex]A=\sqrt{10.24(5.94)(1.64)(2.66)}[/tex][tex]A=\sqrt{265.35}[/tex][tex]A=16.29\ units^{2}[/tex]step 3Find the total area[tex]A=12.24+16.29=28.53\ units^{2}[/tex]