The perimeter of a quadrilateral is 56 cm56 cm. If the first three sides of a quadrilateral, taken in order are 17 cm,16 cm17 cm,16 cm, and 15 cm15 cm respectively, and the angle between fourth side and the third side is a right angle, find the area of the quadrilateral.


Answer:

Area: 180 cm2180 cm2

Step by Step Explanation:
  1. The following picture shows the quadrilateral ABCDABCD,

    The perimeter of the quadrilateral ABCD=56 cmABCD=56 cm
     Therefore ,AB+BC+CD+DA=5617+16+15+DA=5648+DA=56DA=5648DA=8 cm
  2. Let's draw a line AC.
    DA2+DC2
    The ACD is the right angled triangle.
     Therefore, AC2=DA2+DC2AC=DA2+DC2=(8)2+(15)2=17 cm
  3.  The area of the right angled triangle ACD=DA×DC2=8×152=60 cm2
  4. Now, we can see that, this quadrilateral consists of the triangles ACD and ABC.
    The area of the ABC can be calculated using Heron's formula since all sides of the triangle are known.
    S=AB+BC+CA2=17+16+172=25 cm.
     The area of the ABC=S(SAB)(SBC)(SCA)=25(2517)(2516)(2517)=120 cm2
  5.  The area of the quadrilateral ABCD=Area(ACD)+Area(ABC)=60+120=180 cm2

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