Mathematics
In the following figure, OAB is a triangle and AB // DC.
If the area of △ CAD = 140 cm2 and the area of △ ODC = 172 cm2, find
(i) the area of △ DBC
(ii) the area of △ OAC
(iii) the area of △ ODB
Answer
(i) We know that,
The area of triangles on the same base and between the same parallel lines are equal.
Since, △ DBC and △ CAD have same base CD and between the same parallel lines BA and CD.
∴ Area of △ DBC = Area of △ CAD = 140 cm2.
Hence, area of △ DBC = 140 cm2.
(ii) From figure,
⇒ Area of △ OAC = Area of △ CAD + Area of △ ODC
⇒ Area of △ OAC = 140 + 172 = 312 cm2.
Hence, area of △ OAC = 312 cm2.
(iii) From figure,
⇒ Area of △ ODB = Area of △ DBC + Area of △ ODC
⇒ Area of △ ODB = 140 + 172 = 312 cm2.
Hence, area of △ ODB = 312 cm2.
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