The sides of a quadrilateral, taken in order are 13 cm,10 cm,12 cm, and 5 cm respectively. The angle contained by the last two sides is a right angle. Find the area of the quadrilateral.


Answer:

Area: 90 cm2

Step by Step Explanation:
  1. The following picture shows the quadrilateral ABCD,
  2. Let's draw a line AC.
    AD2+DC2
    The ACD is the right-angled triangle.
     Therefore, AC2=AD2+DC2AC=AD2+DC2=(5)2+(12)2=13 cm
  3.  The area of the right-angled triangle ACD=AD×DC2 =5×122=30 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=13+10+132=18 cm.
     The area of the ABC=S(SAB)(SBC)(SCA)=18(1813)(1810)(1813)=60 cm2
  5.  The area of the quadrilateral ABCD=Area(ACD)+Area(ABC)=30+60=90 cm2

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