In a trapezium PQRS, PQ is parallel to RS and diagonals PR and QS intersect at O. If PQ = 4 cm. SR = 10 cm, then what is area(ΔPOQ) : area(ΔSOR) ?
Answer & explanation
Correct answer: option 3
In \(\Delta \)POQ and \(\Delta \)SOR
\(\angle\)RSO = \(\angle\)PQO (Alternate angles)
\(\angle\)SRO = \(\angle\)QPO (Alternate angles)
\(\Delta \)POQ is similar to \(\Delta \)SOR
Now,
\(\frac{area\;of\;POQ}{area \;of\; SOR}\) = (\(\frac{PQ}{SR}\)) 2
= (\(\frac{4}{10}\)) 2 = \(\frac{16}{100}\) = \(\frac{4}{25}\)
Therefore, required ratio 4 : 25.