Quadrilateral has side lengths

MATHEMATICS · Subjective · CBSE · Mathematics · Heron's Formula · Heron's Formula

Problem

Quadrilateral

ABCD

has side lengths

AB = 7\,\text{cm},\; BC = 8\,\text{cm},\; CD = 5\,\text{cm},\; DA = 6\,\text{cm}

. The diagonal

AC

measures

9\,\text{cm}

. (i) Calculate the area of

\triangle ABC

. (ii) Calculate the area of

\triangle ADC

. (iii) Hence, determine the area of quadrilateral

ABCD