Let ABCD be a quadrilateral and AC,BD be diagonals. The length of BD=20cm and the heights of the triangles ABD and BCD are, respectively, 6cm and 8cm. Find the area of the quadrilateral ABCD (in cm
2
).
- A140
- B120
- C148
- D128
Solution & Step-by-step Explanation
The diagonal BD divides the quadrilateral ABCD into two triangles: △ABD and △BCD.
The total area of the quadrilateral ABCD is the sum of the areas of these two triangles.
Area(ABCD)=Area(△ABD)+Area(△BCD)
The area of a triangle is given by
2
1
×base×height. Here, the common base is BD=20cm.
Area(△ABD)=
2
1
×BD×h
1
=
2
1
×20×6=60cm
2
Area(△BCD)=
2
1
×BD×h
2
=
2
1
×20×8=80cm
2
Total Area=60+80=140cm
2
The total area of the quadrilateral ABCD is the sum of the areas of these two triangles.
Area(ABCD)=Area(△ABD)+Area(△BCD)
The area of a triangle is given by
2
1
×base×height. Here, the common base is BD=20cm.
Area(△ABD)=
2
1
×BD×h
1
=
2
1
×20×6=60cm
2
Area(△BCD)=
2
1
×BD×h
2
=
2
1
×20×8=80cm
2
Total Area=60+80=140cm
2