Mathematics 4024 · O Level · Area and perimeter

Area and perimeter — practice question

In trapezium $ABCD$, $AB$ runs parallel to $DC$. $DB$ and $AC$ are straight lines.
(a(i))[1]

Explain why triangle $ACB$ has the same area as triangle $ADB$.

(a(ii)(a))[1]

Name a triangle that is equal in area to triangle $HFK$.

(a(ii)(b))[1]

Hence show that triangle $HEK$ has the same area as quadrilateral $HEFG$.

(b(i))[2]

Complete the proof showing that $\angle SMQ = x^\circ$.

(b(ii))[2]

Prove that $\angle PRM$ equals $y^\circ$.

(b(iii))[3]

Complete the following statement, giving your reasons. The triangles $PRM$ and $QSM$ are ................................

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