<p>In the diagram below, \(PQRS\) is a trapezium in which \(PQ\) is parallel to \(SR\).</p>
<div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/pasted/1767509342044-k5l5rli3o1d.png" style="max-width: min(350px, 100%); height: auto; display: block;" alt="Trapezium PQRS with diagonals PR and QS intersecting at point T. PQ is 12 cm, SR is 30 cm, and QT is 5 cm." class="aligncenter custom-width" /></figure></div>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Prove that&nbsp;\(\Delta PQT\) is similar to \(\Delta RST\).</span></div></li><li><div class="list-item-paragraph">Given that&nbsp;\(PQ = 12\text{ cm}\), \(SR = 30\text{ cm}\) and \(QT = 5\text{ cm}\),</div><ol class="abc-list"><li><div class="list-item-paragraph">calculate \(ST\) ,</div></li><li><div class="list-item-paragraph">find the value of \(\frac{\text{Area of}\hspace{0.5em} \Delta PQT}{\text{Area of}\hspace{0.5em} \Delta RST}\) ,</div></li><li><div class="list-item-paragraph">find the value of \(\frac{\text{Area of}\hspace{0.5em} \Delta PQT}{\text{Area of}\hspace{0.5em} \Delta QTR}\) .</div></li></ol></li></ol>

In the diagram below, \(PQRS\) is a trapezium in which \(PQ\) is parallel to \(SR\).

Prove that \(\Delta PQT\) is similar to \(\Delta RST\).

Given that \(PQ = 12\text{ cm}\), \(SR = 30\text{ cm}\) and \(QT = 5\text{ cm}\),\n\n(a) calculate \(ST\) ,\n\n(b) find the value of \(\frac{\text{Area of } \Delta PQT}{\text{Area of } \Delta RST}\) ,\n\n(c) find the value of \(\frac{\text{Area of } \Delta PQT}{\text{Area of } \Delta QTR}\) .

Given that \(PQ = 12\text{ cm}\), \(SR = 30\text{ cm}\) and \(QT = 5\text{ cm}\),

Deductive Analysis of Area Ratios in Parallel and Similar Configurations

Deductive Analysis of Area Ratios in Parallel and Similar Configurations

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