Question

In the given figure, ABCD is a quadrilateral. A line through D, parallel to AC, meets BC produced in P. Prove that:

(i) Area ($\square$ ABCD) = Area ($△$ PAB)

(ii) If the area of $△$ DAC is 23 sq.cm, then what will be the area of $△$ PAC ?

Answer 1

(i) Here $△$DAC and $△$PAC are on the same base AC and between parallel lines AC and DP
Area ($△$DAC) = Area ($△$PAC)

Adding Area($△$ACB) on both sides, we have,

Area ($△$DAC) + Area ($△$ACB) = Area($△$PAC) + Area ($△$ACB)

Area ($\square$ ABCD)=Area($△$APB)

(ii) Here $△$DAC and $△$PAC are on the same base AC and between parallel lines AC and DP

Area ($△$DAC) = Area ($△$PAC)

$\therefore$ Area ($△$PAC) = 23 sq.cm