Mathematics

Problem

Triangle

ABC

encloses an area of

96\,\text{cm}^2

. Points

D

E

and

P

are the midpoints of

AB

AC

and

BC

respectively. Quadrilateral

BDEP

is formed by joining the points

B

D

E

and

P

in that order. a. (i) Without measuring any lengths, find the area of quadrilateral

BDEP

. b. (ii) Determine the area of triangle

DEP