Find the area of a quadrilateral ABCD where AB = 9 cm, BC = 10 cm, CD = 8 cm, AD = 15 cm, and AC = 17 cm.


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Answer:

96 cm2

Step by Step Explanation:
  1. The following picture shows the quadrilateral ABCD,
  2. Let's draw the diagonal AC in the quadrilateral ABCD,
  3. Now, we can see that, this quadrilateral consists of two triangles, i.e. ΔABC and ΔACD, the area of each triangle can be calculated using Heron's formula since the length of all sides of the triangles are known.
  4. The area of the ΔABC can be calculated using Heron's formula.
    S =  
    AB + BC + AC
    2
     
    =  
    9 + 10 + 17
    2
     
    = 18 cm.
    The area of the ΔABC = √S(S - AB)(S - BC)(S - AC)
    = √18(18 - 9)(18 - 10)(18 - 17)
    = 36 cm2
  5. Similarly, the area of the ΔACD can be calculated using Heron's formula.
    S =  
    AC + CD + AD
    2
     
    =  
    17 + 8 + 15
    2
     
    = 20 cm.
    The area of the ΔACD = √S(S - AC)(S - CD)(S - AD)
    = √20(20 - 9)(20 - 10)(20 - 17)
    = 60 cm2
  6. The area of the quadrilateral ABCD = The area of the ΔABC + The area of the ΔACD
    = 36 + 60
    = 96 cm2

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