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 ADC
we know that
Heron'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]
where
p is half the perimeter
[tex]p=\frac{a+b+c}{2}[/tex]
step 1
Find the area of triangle ABD
we 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 2
Find the area of triangle ADC
we 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 3
Find the total area
[tex]A=12.24+16.29=28.53\ units^{2}[/tex]
