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
- The following picture shows the quadrilateral ABCD,
- Let's draw a line AC.
√AD2+DC2
The △ACD is the right-angled triangle.
Therefore, AC2=AD2+DC2⟹AC=√AD2+DC2=√(5)2+(12)2=13 cm - The area of the right-angled triangle △ACD=AD×DC2 =5×122=30 cm2
- 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(S−AB)(S−BC)(S−CA)=√18(18−13)(18−10)(18−13)=60 cm2 - The area of the quadrilateral ABCD=Area(△ACD)+Area(△ABC)=30+60=90 cm2