Question

a park is the size of a quadrilateral ABCD . in which angle c= 90°, AB=9m, BC=12m, CD=5m & AD=8m . find the area of park with explain from hero's formula​

Answer 1

Step-by-step explanation:

ABCD IS A PARK

DRAW A DIAGONAL BD

IN RIGHT ANGLED TRIANGLE BCD

BY USING PYTHAGORES THEOREM

BD^2=BC^2+CD^2

BD^2=(12)^2+(5)^2

BD^2=144+25

BD^2=169

BD×BD=13×13

BD=13cm

Area of Triangle BCD

=1/2bh

=1/2×12×5

=6×5

=30cm^2

In Triangle ABD

a=9,b=8,c=13

S=a+b+c/2

S=9+8+13/2

S=30/2

S=15cm

Area of Triangle ABD

By using HERONS formula

Area=whole root S(S-a)(S-b)(S-c)

=whole root 15(15-9)(15-8)(15-13)

=whole root 15×6×7×2

=whole root 1260

=6 root 35

AREA OF TRIANGLE ABD=6 root 35

AREA OF ABCD=AREA OF ABD+

AREA OF BCD

AREA OF ABCD=6 root35+30

=6×5.916+30 (root35=5.916)

=35.496cm^2+30cm^2

=65.496cm^2

THE AREA OF THE PARK IS=65.496cm^2