Question

Find the area of quadrilateral ABCD. A. 27.28 units² B. 33.08 units² C. 28.53 units² D. 26.47 units²

Answer 1

Answer:

$\boxed{ \boxed{ \bold{ \purple{ \sf{28.53 \: {units}^{2} }}}}}$

Option C is the correct option.

Step-by-step explanation:

For ABD

$\sf{ = \frac{2.89 + 8.59 + 8.6}{2} }$

$\sf{ = \frac{20.08}{2} }$

$\sf{ = 10.04}$

∆ ABD = $\sf{ = \sqrt{10.04(10.04 - 2.89)(10.04 - 8.59)(10.04 - 8.6)} }$

$\sf{ = \sqrt{10.04 \times 7.15 \times 1.45 \times 1.44 }}$

$\sf{ = \sqrt{149.8891} }$

$\sf{ = 12.2429}$

For ∆ ACD ,

$\sf{s = \frac{8.6 + 4.3 + 7.58}{2} }$

$\sf{ = \frac{20.48}{2} }$

$\sf{ = 10.24}$

∆ ACD = $\sf{ = \sqrt{10.24(10.24 - 8.6)(10.24 - 4.3)(10.24 - 7.58} }$

$\sf{ \sqrt{10.24 \times 1.64 \times 5.94 \times 2.66} }$

$\sf{ = \sqrt{265.3456} }$

$\sf{ = 16.2894}$

Area of quadrilateral ABCD = $\sf{12.2429 + 16.2894}$

$\sf{ = 28.5323}$

$\sf{ = 28.53}$ units ²

Hope I helped!

Best regards!