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

`\boxed{ \boxed{ \bold{ \purple{ \sf{28.53 \: {units}^(2) }}}}}`

Option C is the correct option.

Explanation:

For ABD

`\sf{ = (2.89 + 8.59 + 8.6)/(2) }`

`\sf{ = (20.08)/(2) }`

`\sf{ = 10.04}`

∆ ABD =
`\sf{ = √(10.04(10.04 - 2.89)(10.04 - 8.59)(10.04 - 8.6)) }`

`\sf{ = √(10.04 * 7.15 * 1.45 * 1.44 )}`

`\sf{ = √(149.8891) }`

`\sf{ = 12.2429}`

For ∆ ACD ,

`\sf{s = (8.6 + 4.3 + 7.58)/(2) }`

`\sf{ = (20.48)/(2) }`

`\sf{ = 10.24}`

∆ ACD =
`\sf{ = √(10.24(10.24 - 8.6)(10.24 - 4.3)(10.24 - 7.58) }`

`\sf{ √(10.24 * 1.64 * 5.94 * 2.66) }`

`\sf{ = √(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!