Mathematics

Problem

In a park, a quadrilateral flower bed

ABCD

has sides

AB = 9\,\text{m}

BC = 10\,\text{m}

CD = 11\,\text{m}

DA = 12\,\text{m}

and diagonal

AC = 13\,\text{m}

. a. (i) Determine the area of

\triangle ABC

. b. (ii) Determine the area of

\triangle ADC

. c. (iii) Hence find the total area of the flower bed

ABCD

. d. (iv) The gardener plans to plant roses only in

\triangle ABC

. What percentage of the flower-bed area will remain for other plants?