Question

Find the area of quadrilateral ABCD. [Hint: the diagonal divides the quadrilateral into two triangles.]

Answer 1

Answer:

Option B $28.53\ units^{2}$

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:

$A=\sqrt{p(p-a)(p-b)(p-c)}$

where

p is half the perimeter

$p=\frac{a+b+c}{2}$

step 1

Find the area of triangle ABD

we have

$a=AB=2.89\ units$

$b=BD=8.59\ units$

$c=DA=8.6\ units$

Find the half perimeter p

$p=\frac{2.89+8.59+8.6}{2}=10.04\ units$

Find the area

$A=\sqrt{10.04(10.04-2.89)(10.04-8.59)(10.04-8.6)}$

$A=\sqrt{10.04(7.15)(1.45)(1.44)}$

$A=\sqrt{149.89}$

$A=12.24\ units^{2}$

step 2

Find the area of triangle ADC

we have

$a=AC=4.3\ units$

$b=AD=8.6\ units$

$c=DC=7.58\ units$

Find the half perimeter p

$p=\frac{4.3+8.6+7.58}{2}=10.24\ units$

Find the area

$A=\sqrt{10.24(10.24-4.3)(10.24-8.6)(10.24-7.58)}$

$A=\sqrt{10.24(5.94)(1.64)(2.66)}$

$A=\sqrt{265.35}$

$A=16.29\ units^{2}$

step 3

Find the total area

$A=12.24+16.29=28.53\ units^{2}$